Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Contents of Volume 31, Number 2
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The independence of certain axioms of structures in sets: Japheth Hall; Proc. Amer. Math. Soc. 31 (1972), 317-325; DOI: https://doi.org/10.1090/S0002-9939-1972-0291047-X; PDF

Separation of nonassociates by valuations: David E. Brown and Max D. Larsen; Proc. Amer. Math. Soc. 31 (1972), 326-332; DOI: https://doi.org/10.1090/S0002-9939-1972-0289506-9; PDF

Solution of certain matrix equations: John Jones; Proc. Amer. Math. Soc. 31 (1972), 333-339; DOI: https://doi.org/10.1090/S0002-9939-1972-0292863-0; PDF

Representations of Euler classes: Howard Osborn; Proc. Amer. Math. Soc. 31 (1972), 340-346; DOI: https://doi.org/10.1090/S0002-9939-1972-0300303-8; PDF

Divinsky’s radical: Patrick N. Stewart; Proc. Amer. Math. Soc. 31 (1972), 347-353; DOI: https://doi.org/10.1090/S0002-9939-1972-0286823-3; PDF

Some applications of differential algebra to ring theory: John Cozzens and Joseph Johnson; Proc. Amer. Math. Soc. 31 (1972), 354-356; DOI: https://doi.org/10.1090/S0002-9939-1972-0289472-6; PDF

A note on zero divisors in group-rings: Jacques Lewin; Proc. Amer. Math. Soc. 31 (1972), 357-359; DOI: https://doi.org/10.1090/S0002-9939-1972-0292957-X; PDF

On groups of exponent four. II: C. K. Gupta and N. D. Gupta; Proc. Amer. Math. Soc. 31 (1972), 360-362; DOI: https://doi.org/10.1090/S0002-9939-1972-0289631-2; PDF

The Lie algebra of the structure group of a power-associative algebra.: D. R. Scribner; Proc. Amer. Math. Soc. 31 (1972), 363-367; DOI: https://doi.org/10.1090/S0002-9939-1972-0288154-4; PDF

Algebraic algebras with involution: Susan Montgomery; Proc. Amer. Math. Soc. 31 (1972), 368-372; DOI: https://doi.org/10.1090/S0002-9939-1972-0288149-0; PDF

A generalization of Mori’s theorem: Chin-pi Lu; Proc. Amer. Math. Soc. 31 (1972), 373-375; DOI: https://doi.org/10.1090/S0002-9939-1972-0286786-0; PDF

On algebras satisfying the identity $(yx)x+x(xy)=2(xy)x$: Robert A. Chaffer; Proc. Amer. Math. Soc. 31 (1972), 376-380; DOI: https://doi.org/10.1090/S0002-9939-1972-0288153-2; PDF

The class number of $Q(\surd -p)$, for $P\equiv 1 (\textrm {mod}\ 8)$ a prime: Ezra Brown; Proc. Amer. Math. Soc. 31 (1972), 381-383; DOI: https://doi.org/10.1090/S0002-9939-1972-0289455-6; PDF

Dirichlet $L$-functions and primitive characters: Tom M. Apostol; Proc. Amer. Math. Soc. 31 (1972), 384-386; DOI: https://doi.org/10.1090/S0002-9939-1972-0285499-9; PDF

The distribution of absolutely irreducible polynomials in several indeterminates: M. L. Fredman; Proc. Amer. Math. Soc. 31 (1972), 387-390; DOI: https://doi.org/10.1090/S0002-9939-1972-0286779-3; PDF

Union conditions in Noether lattices: Johnny A. Johnson; Proc. Amer. Math. Soc. 31 (1972), 391-394; DOI: https://doi.org/10.1090/S0002-9939-1972-0294188-6; PDF

Which abelian groups can support a directed, interpolation order?: A. M. W. Glass; Proc. Amer. Math. Soc. 31 (1972), 395-400; DOI: https://doi.org/10.1090/S0002-9939-1972-0289389-7; PDF

Characterization of rings using quasiprojective modules. III: Jonathan S. Golan; Proc. Amer. Math. Soc. 31 (1972), 401-408; DOI: https://doi.org/10.1090/S0002-9939-1972-0302700-3; PDF

An embedding theorem for commutative lattice-ordered domains: Stuart A. Steinberg; Proc. Amer. Math. Soc. 31 (1972), 409-416; DOI: https://doi.org/10.1090/S0002-9939-1972-0285464-1; PDF

Separating $p$-bases and transcendental extension fields: J. N. Mordeson and B. Vinograde; Proc. Amer. Math. Soc. 31 (1972), 417-422; DOI: https://doi.org/10.1090/S0002-9939-1972-0289465-9; PDF

An extension of the Noether-Deuring theorem: Klaus W. Roggenkamp; Proc. Amer. Math. Soc. 31 (1972), 423-426; DOI: https://doi.org/10.1090/S0002-9939-1972-0286839-7; PDF

Determination of $k_{n} (n\geq 3)$ for global fields: Richard Elman and T.-Y. Lam; Proc. Amer. Math. Soc. 31 (1972), 427-428; DOI: https://doi.org/10.1090/S0002-9939-1972-0289604-X; PDF

A note on finitely generated ideals which are locally principal: James W. Brewer and Edgar A. Rutter; Proc. Amer. Math. Soc. 31 (1972), 429-432; DOI: https://doi.org/10.1090/S0002-9939-1972-0289480-5; PDF

On the exponent of the ideal class groups of complex quadratic fields.: David W. Boyd and H. Kisilevsky; Proc. Amer. Math. Soc. 31 (1972), 433-436; DOI: https://doi.org/10.1090/S0002-9939-1972-0289454-4; PDF

Monotonicity of positive semidefinite Hermitian matrices: Russell Merris and Stephen Pierce; Proc. Amer. Math. Soc. 31 (1972), 437-440; DOI: https://doi.org/10.1090/S0002-9939-1972-0285556-7; PDF

On the existence of fixed points in a totally ordered set: F. T. Metcalf and T. H. Payne; Proc. Amer. Math. Soc. 31 (1972), 441-444; DOI: https://doi.org/10.1090/S0002-9939-1972-0286722-7; PDF

Principal ideals in the ideal lattice: H. Subramanian; Proc. Amer. Math. Soc. 31 (1972), 445; DOI: https://doi.org/10.1090/S0002-9939-1972-0284424-4; PDF

Starlike meromorphic functions: James Miller; Proc. Amer. Math. Soc. 31 (1972), 446-452; DOI: https://doi.org/10.1090/S0002-9939-1972-0288267-7; PDF

Positive solutions of positive linear equations: Paul Nelson; Proc. Amer. Math. Soc. 31 (1972), 453-457; DOI: https://doi.org/10.1090/S0002-9939-1972-0288605-5; PDF

The spectra of unbounded hyponormal operators: C. R. Putnam; Proc. Amer. Math. Soc. 31 (1972), 458-464; DOI: https://doi.org/10.1090/S0002-9939-1972-0291848-8; PDF

Isometries of $H^{p}$ spaces of the torus: Nand Lal and Samuel Merrill; Proc. Amer. Math. Soc. 31 (1972), 465-471; DOI: https://doi.org/10.1090/S0002-9939-1972-0296676-5; PDF

A representation theorem for $L^{p}$ spaces: Marek Kanter; Proc. Amer. Math. Soc. 31 (1972), 472-474; DOI: https://doi.org/10.1090/S0002-9939-1972-0290088-6; PDF

On the smoothness of eigenfunctions of hyponormal singular integral operators: Kevin Clancey; Proc. Amer. Math. Soc. 31 (1972), 475-479; DOI: https://doi.org/10.1090/S0002-9939-1972-0284873-4; PDF

Stone’s theorem for a group of unitary operators over a Hilbert space: Habib Salehi; Proc. Amer. Math. Soc. 31 (1972), 480-484; DOI: https://doi.org/10.1090/S0002-9939-1972-0300128-3; PDF

Measurability of functions in product spaces: Kohur Gowrisankaran; Proc. Amer. Math. Soc. 31 (1972), 485-488; DOI: https://doi.org/10.1090/S0002-9939-1972-0291403-X; PDF

A uniform asymptotic turning point theory for second order linear ordinary differential equations: Erich Zauderer; Proc. Amer. Math. Soc. 31 (1972), 489-494; DOI: https://doi.org/10.1090/S0002-9939-1972-0288365-8; PDF

Equivalent types of invariant means on locally compact groups: P. F. Renaud; Proc. Amer. Math. Soc. 31 (1972), 495-498; DOI: https://doi.org/10.1090/S0002-9939-1972-0304974-1; PDF

On asymptotic behavior of perturbed nonlinear systems: R. E. Fennell and T. G. Proctor; Proc. Amer. Math. Soc. 31 (1972), 499-504; DOI: https://doi.org/10.1090/S0002-9939-1972-0287099-3; PDF

Multiplier operators on $B^{\ast }$-algebras: B. D. Malviya and B. J. Tomiuk; Proc. Amer. Math. Soc. 31 (1972), 505-510; DOI: https://doi.org/10.1090/S0002-9939-1972-0305085-1; PDF

Dual necklaces of $n$-dimensional cubes: Kenneth Kalmanson; Proc. Amer. Math. Soc. 31 (1972), 511-516; DOI: https://doi.org/10.1090/S0002-9939-1972-0285993-0; PDF

Extending congruence relations: Peter Krauss; Proc. Amer. Math. Soc. 31 (1972), 517-520; DOI: https://doi.org/10.1090/S0002-9939-1972-0285470-7; PDF

A property of arithmetic sets: Hisao Tanaka; Proc. Amer. Math. Soc. 31 (1972), 521-524; DOI: https://doi.org/10.1090/S0002-9939-1972-0286661-1; PDF

Elementary extensions of linear topological abelian groups: R. G. Phillips and P. L. Sperry; Proc. Amer. Math. Soc. 31 (1972), 525-528; DOI: https://doi.org/10.1090/S0002-9939-1972-0288212-4; PDF

The Wall invariant of certain $S^{1}$ bundles: Douglas R. Anderson; Proc. Amer. Math. Soc. 31 (1972), 529-535; DOI: https://doi.org/10.1090/S0002-9939-1972-0287545-5; PDF

The bordism ring of manifolds with involution: J. C. Alexander; Proc. Amer. Math. Soc. 31 (1972), 536-542; DOI: https://doi.org/10.1090/S0002-9939-1972-0290379-9; PDF

A product theorem for $H$-group fibrations: F. H. Croom; Proc. Amer. Math. Soc. 31 (1972), 543-549; DOI: https://doi.org/10.1090/S0002-9939-1972-0290368-4; PDF

The hyperspace of a pseudoarc is a Cantor manifold: Togo Nishiura and Choon Jai Rhee; Proc. Amer. Math. Soc. 31 (1972), 550-556; DOI: https://doi.org/10.1090/S0002-9939-1972-0290337-4; PDF

An index for set-valued maps in infinite-dimensional spaces: Stephen A. Williams; Proc. Amer. Math. Soc. 31 (1972), 557-563; DOI: https://doi.org/10.1090/S0002-9939-1972-0287535-2; PDF

Equivariant bordism and cyclic groups: Peter S. Landweber; Proc. Amer. Math. Soc. 31 (1972), 564-570; DOI: https://doi.org/10.1090/S0002-9939-1972-0296969-1; PDF

Regular compactifications of convergence spaces: G. D. Richardson and D. C. Kent; Proc. Amer. Math. Soc. 31 (1972), 571-573; DOI: https://doi.org/10.1090/S0002-9939-1972-0286074-2; PDF

On the countably generated $z$-ideals of $C(X)$: G. De Marco; Proc. Amer. Math. Soc. 31 (1972), 574-576; DOI: https://doi.org/10.1090/S0002-9939-1972-0288563-3; PDF

A compactification of locally compact spaces: F. W. Lozier; Proc. Amer. Math. Soc. 31 (1972), 577-579; DOI: https://doi.org/10.1090/S0002-9939-1972-0286072-9; PDF

$H$-spaces which are co-$H$-spaces: Robert W. West; Proc. Amer. Math. Soc. 31 (1972), 580-582; DOI: https://doi.org/10.1090/S0002-9939-1972-0285006-0; PDF

Sets accessible at each point only by wild arcs: Gary Glenn Miller; Proc. Amer. Math. Soc. 31 (1972), 583-590; DOI: https://doi.org/10.1090/S0002-9939-1972-0284992-2; PDF

Rigid pairs of long arcs: Gary G. Miller; Proc. Amer. Math. Soc. 31 (1972), 591-594; DOI: https://doi.org/10.1090/S0002-9939-1972-0290336-2; PDF

Fixed point theorems for certain classes of multifunctions: R. E. Smithson; Proc. Amer. Math. Soc. 31 (1972), 595-600; DOI: https://doi.org/10.1090/S0002-9939-1972-0288750-4; PDF

On Spanier’s higher order operations: Yuh-ching Chen; Proc. Amer. Math. Soc. 31 (1972), 601-604; DOI: https://doi.org/10.1090/S0002-9939-1972-0288758-9; PDF

An algebraic proof that $[\Omega ^{U}]_{2}=\mathfrak {N}^{2}$: Don Porter; Proc. Amer. Math. Soc. 31 (1972), 605-608; DOI: https://doi.org/10.1090/S0002-9939-1972-0288773-5; PDF

Products of uncountably many $k$-spaces: N. Noble; Proc. Amer. Math. Soc. 31 (1972), 609-612; DOI: https://doi.org/10.1090/S0002-9939-1972-0287503-0; PDF

$C$-embedded subsets of products: N. Noble; Proc. Amer. Math. Soc. 31 (1972), 613-614; DOI: https://doi.org/10.1090/S0002-9939-1972-0284978-8; PDF

Pseudo-isotopies of arcs and knots: Carl D. Sikkema; Proc. Amer. Math. Soc. 31 (1972), 615-616; DOI: https://doi.org/10.1090/S0002-9939-1972-0286094-8; PDF

Inadequacy of ordinary homology theory: T. Y. Lin; Proc. Amer. Math. Soc. 31 (1972), 617-619; DOI: https://doi.org/10.1090/S0002-9939-1972-0307241-5; PDF

A note on one-dimensional attracting sets in the three-sphere: Joel C. Gibbons; Proc. Amer. Math. Soc. 31 (1972), 620-622; DOI: https://doi.org/10.1090/S0002-9939-1972-0292109-3; PDF

A decomposition theorem for closed compact connected P. L. $n$-manifolds: B. G. Casler; Proc. Amer. Math. Soc. 31 (1972), 623-624; DOI: https://doi.org/10.1090/S0002-9939-1972-0290372-6; PDF

Quotient groups of topological groups with no small subgroups: Sidney A. Morris; Proc. Amer. Math. Soc. 31 (1972), 625-626; DOI: https://doi.org/10.1090/S0002-9939-1972-0293000-9; PDF

Another fixed point theorem for plane continua: Charles L. Hagopian; Proc. Amer. Math. Soc. 31 (1972), 627-628; DOI: https://doi.org/10.1090/S0002-9939-1972-0286093-6; PDF

A holomorphic function having a discontinuous inverse: T. J. Suffridge; Proc. Amer. Math. Soc. 31 (1972), 629-630; DOI: https://doi.org/10.1090/S0002-9939-1972-0284813-8; PDF

Pólya’s property $W$ and factorization—A short proof: Robert Ristroph; Proc. Amer. Math. Soc. 31 (1972), 631-632; DOI: https://doi.org/10.1090/S0002-9939-1972-0288338-5; PDF

Cyclic vectors of induced representations: A. Hulanicki and T. Pytlik; Proc. Amer. Math. Soc. 31 (1972), 633-634; DOI: https://doi.org/10.1090/S0002-9939-1972-0289717-2; PDF

Spherical images of convex surfaces: M. do Carmo and B. Lawson; Proc. Amer. Math. Soc. 31 (1972), 635-636; DOI: https://doi.org/10.1090/S0002-9939-1972-0293548-7; PDF

Vanishing of Stiefel-Whitney classes: W. A. Sutherland; Proc. Amer. Math. Soc. 31 (1972), 637; DOI: https://doi.org/10.1090/S0002-9939-1972-0292081-6; PDF

Erratum to Volume 27; Erratum to Volume 29: Proc. Amer. Math. Soc. 31 (1972), 638-638; DOI: https://doi.org/10.1090/S0002-9939-72-99955-8; PDF