An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, then M is semi-...

This is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay a foundation for this study. We formulate and study notions of quasi module and S-quasi module for a G1-vertex algebra V , where S is a quantum Yang-Baxter operator on V . We also formulate and study a notion of qu...

In this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. Several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given. Then we investigate for a ring $R$, when any fi...

an r-module m is called epi-retractable if every submodule of mr is a homomorphic image of m. it is shown that if r is a right perfect ring, then every projective slightly compressible module mr is epi-retractable. if r is a noetherian ring, then every epi-retractable right r-module has direct sum of uniform submodules. if endomorphism ring of a module mr is von-neumann regular, then m is semi-...

The notion of a quasi-free Hilbert module over a function algebra A consisting of holomorphic functions on a bounded domain Ω in complex m space is introduced. It is shown that quasi-free Hilbert modules correspond to the completion of the direct sum of a certain number of copies of the algebra A. A Hilbert module is said to be weakly regular (respectively, regular) if there exists a module map...

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

There is a well-known equivalence between the homotopy types of connected CW-spaces X with πnX=0 for n 6= 1, 2 and the quasi-isomorphism classes of crossed modules ∂ : M → P [16]. When the homotopy groups π1X and π2X are finite one can represent the homotopy type of X by a crossed module in which M and P are finite groups. We define the order of such a crossed module to be |∂| = |M | × |P |, an...