Indecomposable decompositions and the minimal direct summand containing the nilpotents
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- by G. F. Birkenmeier PDF
- Proc. Amer. Math. Soc. 73 (1979), 11-14 Request permission
Abstract:
It is well known that an indecomposable right ideal decomposition of a ring is not necessarily unique. In this paper we show that the reduced right ideals of such a decomposition are unique up to isomorphism and the remainder of the decomposition forms the unique MDSN. In the main theorem we use triangular matrices to prove that a ring with an indecomposable decomposition is basically composed of a nilpotent ring, a ring (containing a unity) with an indecomposable decomposition which equals its MDSN, and a direct sum of indecomposable reduced rings with unity.References
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G. F. Birkenmeier, A decomposition theory of rings, Ph.D. Thesis, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, 1975.
- G. F. Birkenmeier, Self-injective rings and the minimal direct summand containing the nilpotents, Comm. Algebra 4 (1976), no. 8, 705–721. MR 419526, DOI 10.1080/00927877608822132
- Joachim Lambek, Lectures on rings and modules, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1966. With an appendix by Ian G. Connell. MR 0206032
- B. L. Osofsky, A remark on the Krull-Schmidt-Azumaya theorem, Canad. Math. Bull. 13 (1970), 501–505. MR 274518, DOI 10.4153/CMB-1970-091-6
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 11-14
- MSC: Primary 16A32
- DOI: https://doi.org/10.1090/S0002-9939-1979-0512048-6
- MathSciNet review: 512048