Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Indecomposable decompositions and the minimal direct summand containing the nilpotents


Author: G. F. Birkenmeier
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A32

Retrieve articles in all journals with MSC: 16A32


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0512048-6
Keywords: Nilpotent elements, reduced ring
Article copyright: © Copyright 1979 American Mathematical Society