Regularity of semilattice sums of rings
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- by John Janeski and Julian Weissglass
- Proc. Amer. Math. Soc. 39 (1973), 479-482
- DOI: https://doi.org/10.1090/S0002-9939-1973-0316495-1
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Abstract:
If $R$ is a supplementary semilattice sum of subrings ${R_\alpha },\alpha \in \Omega$, then $R$ is regular if and only if each ${R_\alpha }$ is regular.References
- A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR 0132791
- Nathan Divinsky, Rings and radicals, Mathematical Expositions, No. 14, University of Toronto Press, Toronto, Ont., 1965. MR 0197489
- Irving Kaplansky, Fields and rings, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0269449
- W. D. Munn, On semigroup algebras, Proc. Cambridge Philos. Soc. 51 (1955), 1–15. MR 66355, DOI 10.1017/s0305004100029868
- Mohan S. Putcha, Semilattice decompositions of semigroups, Semigroup Forum 6 (1973), no. 1, 12–34. MR 369582, DOI 10.1007/BF02389104 J. von Neumann, On regular rings, Proc. Nat. Acad. Sci. U.S.A. 22 (1936), 707-713.
- Julian Weissglass, Regularity of semigroup rings, Proc. Amer. Math. Soc. 25 (1970), 499–503. MR 257251, DOI 10.1090/S0002-9939-1970-0257251-X
- Julian Weissglass, Semigroup rings and semilattice sums of rings, Proc. Amer. Math. Soc. 39 (1973), 471–478. MR 322092, DOI 10.1090/S0002-9939-1973-0322092-4
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 479-482
- MSC: Primary 16A30
- DOI: https://doi.org/10.1090/S0002-9939-1973-0316495-1
- MathSciNet review: 0316495