Goldie-Supplemented Modules

Abstract

. We show that the β * relation is an equivalence relation and has good behaviour with respect to addition of submodules, homomorphisms and supplements. We apply these results to introduce the class of G * -supplemented modules and to investigate this class and the class of H-supplemented modules. These classes are located among various well-known classes of modules related to the class of lifting modules. Moreover these classes are used to explore an open question of S. H. Mohamed and B. J. Mueller. Examples are provided to illustrate and delimit the theory.2000 Mathematics Subject Classification. 16D10, 16D50.

Goldie*-Supplemented Modules – Corrigendum

“…This result follows from [1, Theorem 3.6], [1, Proposition 3.11] and [2, 27.21]. Also, there are a few typos in the paper: (1) on page 42, lines 14 and 22 : replace "supplementing" with "supplemented"; (2) on page 48, line 22 : replace "Msller" with "Müller"; (3) on page 52: in reference [1] replace "Commun." with "Comm."…”

A new approach to H-supplemented modules via homomorphisms

“…After that, in [8], the authors presented some equivalent conditions for a module to be H -supplemented that shows that this class of modules is closely related to the concept of small submodules. One of the nice papers related to H -supplemented modules and their generalizations is [3]. In [3], the authors introduced a new generalization of H -supplemented modules that is Goldie * -supplemented modules via an equivalence relation, namely β * .…”

“…One of the nice papers related to H -supplemented modules and their generalizations is [3]. In [3], the authors introduced a new generalization of H -supplemented modules that is Goldie * -supplemented modules via an equivalence relation, namely β * . Let X and Y be submodules of [16], [17], and [20]).…”

Principally Goldie*-Lifting Modules

“…Lifting modules play an important role in module theory. Also their various generalizations are studied by many authors in [1], [4], [6], [7], [8], [9], [10] [4]).…”