On modules with the absolute direct summand property. (English) Zbl 0853.16008

Burgess, W. D.; Raphael, R.

Jain, S. K. (ed.) et al., Ring theory. Proceedings of the biennial Ohio State-Denison mathematics conference, May 14-16, 1992 dedicated to the memory of H. J. Zassenhaus. Singapore: World Scientific. 137-148 (1993).

Summary: Modules with the absolute direct summand property are studied. These are modules so that each direct sum decomposition is rigid in the following sense: If \(M=A\oplus B\) and \(C\) is a complement of \(A\) then \(M=A\oplus C\). This property, more general than quasi-continuity, does impose structure on \(M\), especially when it is rich in direct sum decompositions. Such modules over left noetherian rings are most amenable to study. The particular module \(_RR\) is examined when \(R\) is left artinian and when it is von Neumann regular.
For the entire collection see [Zbl 0845.00040].

MSC:

16D70	Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
16P40	Noetherian rings and modules (associative rings and algebras)
16E50	von Neumann regular rings and generalizations (associative algebraic aspects)
16P20	Artinian rings and modules (associative rings and algebras)

Keywords:

absolute direct summand property; direct sum decompositions; complements; left Noetherian rings