Rings with subexponential growth and irreducible representations
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- by Ronald S. Irving
- Proc. Amer. Math. Soc. 72 (1978), 445-450
- DOI: https://doi.org/10.1090/S0002-9939-1978-0509232-3
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Abstract:
Some monoids and algebras are constructed with growth which is subexponential but not polynomially bounded. The algebras have homomorphic images which are primitive with polynomially bounded growth, but which do not satisfy a Nullstellensatz-type of property.References
- S. A. Amitsur and C. Procesi, Jacobson-rings and Hilbert algebras with polynomial identities, Ann. Mat. Pura Appl. (4) 71 (1966), 61–72. MR 206044, DOI 10.1007/BF02413733
- H. Bass, The degree of polynomial growth of finitely generated nilpotent groups, Proc. London Math. Soc. (3) 25 (1972), 603–614. MR 379672, DOI 10.1112/plms/s3-25.4.603
- Yves Guivarc’h, Croissance polynomiale et périodes des fonctions harmoniques, Bull. Soc. Math. France 101 (1973), 333–379 (French). MR 369608
- Marshall Hall Jr., Combinatorial theory, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1967. MR 0224481
- Ronald S. Irving, Some primitive group rings, J. Algebra 56 (1979), no. 1, 274–281. MR 527170, DOI 10.1016/0021-8693(79)90338-7
- Martin Lorenz, Primitive ideals of group algebras of supersoluble groups, Math. Ann. 225 (1977), no. 2, 115–122. MR 424862, DOI 10.1007/BF01351715
- John Milnor, Growth of finitely generated solvable groups, J. Differential Geometry 2 (1968), 447–449. MR 244899
- Daniel Quillen, On the endomorphism ring of a simple module over an enveloping algebra, Proc. Amer. Math. Soc. 21 (1969), 171–172. MR 238892, DOI 10.1090/S0002-9939-1969-0238892-4
- Martha K. Smith, Universal enveloping algebras with subexponential but not polynomially bounded growth, Proc. Amer. Math. Soc. 60 (1976), 22–24 (1977). MR 419534, DOI 10.1090/S0002-9939-1976-0419534-5
- Joseph A. Wolf, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Differential Geometry 2 (1968), 421–446. MR 248688
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 445-450
- MSC: Primary 16A06; Secondary 16A16
- DOI: https://doi.org/10.1090/S0002-9939-1978-0509232-3
- MathSciNet review: 509232