let $r$ be an arbitrary ring with identity and $m$ a right $r$-module with $s=$ end$_r(m)$. the module $m$ is called {it rickart} if for any $fin s$, $r_m(f)=se$ for some $e^2=ein s$. we prove that some results of principally projective rings and baer modules can be extended to rickart modules for this general settings.

Lifting modules plays important roles in module theory. H-supplemented are a nice generalization of lifting which have been studied extensively recently. In this article, we introduce proper via images fully invariant submodules. Let F be submodule right Rmodule M. We say that M is IF -H-supplemented case for every endomorphism φ M, there direct summand D such φ(F) + X = if and only It proved d...

A module M is said to belifting if, for anysubmodule N of M, there exists a direct summand X contained in such that N/X small M/X. satisfy the finite internal exchange propertyif, any and sum decomposition M=Lni=1Mi, M′i Mi (i= 1,2, . , n) M=X⊕(Lni=1M′i). In this paper, we first give characterizations forthe square hollow uniform be lifting (extending). addition, solve negatively question "Does...

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre’s problem, was extensively studied befo...

We explain how Queffelec–Sartori’s construction of the HOMFLY-PT link polynomial can be interpreted in terms parabolic Verma modules for \({\mathfrak {gl}_{2n}}\). Lifting to world categorification, we use 2-Verma give a higher representation theory Khovanov–Rozansky’s triply graded homology.

The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary  generalized local cohomology  modules.  Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$  are  finitely generated  $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...