Semigroup rings and semilattice sums of rings
HTML articles powered by AMS MathViewer
- by Julian Weissglass
- Proc. Amer. Math. Soc. 39 (1973), 471-478
- DOI: https://doi.org/10.1090/S0002-9939-1973-0322092-4
- PDF | Request permission
Abstract:
A generalization of the concept of a decomposition of a ring into a direct sum of ideals is introduced. The question of semisimplicity of the ring in terms of the semisimplicity of its summands is investigated. The results are applied to semigroup rings.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
- John Janeski and Julian Weissglass, Regularity of semilattice sums of rings, Proc. Amer. Math. Soc. 39 (1973), 479–482. MR 316495, DOI 10.1090/S0002-9939-1973-0316495-1
- Nathan Jacobson, Structure of rings, Revised edition, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, Providence, R.I., 1964. MR 0222106
- 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
- Mohan S. Putcha and Julian Weissglass, A semilattice decomposition into semigroups having at most one idempotent, Pacific J. Math. 39 (1971), 225–228. MR 304523
- Hans Schneider and Julian Weissglass, Group rings, semigroup rings and their radicals, J. Algebra 5 (1967), 1–15. MR 213453, DOI 10.1016/0021-8693(67)90021-X T. Tamura, Quasi-orders, generalized archimedeanness and semilattice decompositions (submitted).
- Julian Weissglass, Radicals of semigroup rings, Glasgow Math. J. 10 (1969), 85–93. MR 265485, DOI 10.1017/S0017089500000616
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 471-478
- MSC: Primary 20M25
- DOI: https://doi.org/10.1090/S0002-9939-1973-0322092-4
- MathSciNet review: 0322092