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All content in this area was uploaded by Julius Zelmanowitz on Jun 12, 2020
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Density for polyform modules
... A module is said to be polyform if every essential submodule of M is rational in M [6], it is known that a module is uniform if every of its submodule is essential. A module is retractable if Hom (M, X) ≠ 0, for all X submodule of M [14]. A module M is called fully retractable if for every nonzero submodule N of M and every nonzero element g ϵ Hom R ( N,M) we have Hom R (M , N) g ≠ 0 [14]. ...
... A module is retractable if Hom (M, X) ≠ 0, for all X submodule of M [14]. A module M is called fully retractable if for every nonzero submodule N of M and every nonzero element g ϵ Hom R ( N,M) we have Hom R (M , N) g ≠ 0 [14]. The dual of the previous concepts, also introduced and investigated in many works. ...
A module is compressible if it can be embedded in each of its nonzero submodules. A compressible module is critically compressible if it cannot be embedded in any of its proper factors. This concept is a generalization of simple module. In this paper, a new generalization of simple module is introduced and studied, which is a dual to the above concept. A module is co compressible if it is a homomorphic image of each of its non trivial factors, also a co compressible module is critically cocompressible, if it is not a homomorphic image of each of its proper submodules.
... In this section, we generalize results given in [2] and we show that in the class of quasi-projective modules the Zelmanowitz's question has an affirmative answer. We recall the concept of fully retractable that was given in [9]. Definition 2.1. ...
In this paper we consider a problem due to Zel-manowitz. Specifically, we study under what conditions a uniform compressible module whose nonzero endomorphisms are monomor-phisms is critically compressible. We give a positive answer to this problem for the class of nonsingular modules, quasi-projective mod-ules and for modules over rings which are in a certain class of rings which contains at least the commutative rings and left duo rings.
The main purpose of this paper is to introduce the concept of small co compressible modules, as a generalization of co compressible module. A module M is small co compressible(s-co compressible) if it is a homomorphic image of M / N for each small submodule N of M, and M is critically s- co compressible if it is small – co compressible and in addition it is not a homomorphic image of any of its small submodules. The objective of this article is to investigate the properties of the new concepts and study the relationships between them and with the origin concept (co compressible module).
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