Graded rings and Krull orders

Jespers, Eric; Wauters, Paul

doi:10.1090/S0002-9939-1989-0955461-1

Graded rings and Krull orders
HTML articles powered by AMS MathViewer

by Eric Jespers and Paul Wauters

Proc. Amer. Math. Soc. 107 (1989), 309-313

DOI: https://doi.org/10.1090/S0002-9939-1989-0955461-1

PDF | Request permission

Abstract:

Let $R$ be a faithfully $S$-graded ring, where $S$ is a submoniod of a torsion-free commutative group and $S$ has no nontrivial units. In case $R$ is a prime Krull order we give necessary and sufficient conditions for $R$ to be a crossed product (respectively a polynomial ring).

References

David F. Anderson, Graded Krull domains, Comm. Algebra 7 (1979), no. 1, 79–106. MR 514866, DOI 10.1080/00927877908822334
D. D. Anderson and David F. Anderson, Divisibility properties of graded domains, Canadian J. Math. 34 (1982), no. 1, 196–215. MR 650859, DOI 10.4153/CJM-1982-013-3
Marc Chamarie, Anneaux de Krull non commutatifs, J. Algebra 72 (1981), no. 1, 210–222 (French). MR 634623, DOI 10.1016/0021-8693(81)90318-5

Anneaux de Krull non-commutatifs

Leo G. Chouinard II, Krull semigroups and divisor class groups, Canadian J. Math. 33 (1981), no. 6, 1459–1468. MR 645239, DOI 10.4153/CJM-1981-112-x
M. Cohen and S. Montgomery, Group-graded rings, smash products, and group actions, Trans. Amer. Math. Soc. 282 (1984), no. 1, 237–258. MR 728711, DOI 10.1090/S0002-9947-1984-0728711-4
Robert Gilmer, Commutative semigroup rings, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1984. MR 741678
Eric Jespers, On radicals of graded rings and applications to semigroup rings, Comm. Algebra 13 (1985), no. 11, 2457–2472. MR 807485, DOI 10.1080/00927878508823284
Eric Jespers and Paul Wauters, A general notion of noncommutative Krull rings, J. Algebra 112 (1988), no. 2, 388–415. MR 926613, DOI 10.1016/0021-8693(88)90098-1
Hidetoshi Marubayashi, Polynomial rings over Krull orders in simple Artinian rings, Hokkaido Math. J. 9 (1980), no. 1, 63–78. MR 563187, DOI 10.14492/hokmj/1381758228
C. Năstăsescu, E. Nauwelaerts, and F. Van Oystaeyen, Arithmetically graded rings revisited, Comm. Algebra 14 (1986), no. 10, 1991–2017. MR 864568, DOI 10.1080/00927878608823407
P. Wauters, $\Omega$-Krull rings and Gr-$\Omega$-Krull rings in the non-P.I. case, J. Pure Appl. Algebra 32 (1984), no. 1, 95–113. MR 739641, DOI 10.1016/0022-4049(84)90017-3
P. Wauters, Factorial domains and graded rings, Comm. Algebra 17 (1989), no. 4, 827–836. MR 990980, DOI 10.1080/00927878908823761