On AdS-modules with the SIP. (English) Zbl 1373.16013

Mutlu, F. Takil

Bull. Iran. Math. Soc. 41, No. 6, 1355-1363 (2015).

Summary: The class of ads modules with the SIP (briefly, \(SA\)-modules) is studied. Various conditions for a module to be \(SA\)-module are given. It is proved that for a quasi-continuous module \(M\), \(M\) is a UC-module if and only if \(M\) is an \(SA\)-module. Also, it is proved that the direct sum of two \(SA\)-modules as \(R\)-modules is an \(SA\)-module when \(R\) is the sum of the annihilators of these modules.

MSC:

16D70

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)

Keywords:

AdS-modules; summand intersection property; extending modules