Results 1 to 10 of about 33 (32)

Injective and coherent endomorphism rings relative to some matrices

Open Mathematics, 2023
Let MM be a right RR-module with S=End(MR)S={\rm{End}}\left({M}_{R}). Given two cardinal numbers α\alpha and β\beta and a row-finite matrix A∈RFMβ×α(S)A\in {{\rm{RFM}}}_{\beta \times \alpha }\left(S), SM{}_{S}M is called injective relative to AA if ...
Zeng Yuedi
doaj   +1 more source

Strongly Generalized Radical Supplemented Modules

Discussiones Mathematicae - General Algebra and Applications, 2020
We introduce and study strongly generalized radical-supplemented modules (or briefly sgrs-modules). With the notation Radg(R) := ∩{K : K ≤ RR, K is both essential and maximal}, we prove that (under some mild conditions on a ring R) every right R-module ...
Das Soumitra, Buhphang Ardeline M.
doaj   +1 more source

Goldie absolute direct summand rings and modules [PDF]

, 2018
In the present paper, we introduce and study Goldie ADS modules and rings, which subsume two generalizations of Goldie extending modules due to Akalan et al. [3] and ADS-modules due to Alahmadi et al. [7]. A module M will be called a Goldie ADS module if
ȘAHINKAYA, Serap, CONG QUYNH, Truong
core   +1 more source

Projective covers and minimal free resolutions

International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 1, Page 185-192, 1996., 1996
Using a generalization of the definition of the projective cover of a module, a special type of surjective free resolution, known as the projective cover of a complex, may be defined. The projective cover is shown to be a direct summand of every surjective free resolution and to be the direct sum of the minimal free resolution and an exact complex ...
Mark A. Goddard
wiley   +1 more source

Modules which are self-p-injective relative to projection invariant submodules

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017
In this article, we focus on modules M such that every homomorphism from a projection invariant submodule of M to M can be lifted to M. Although such modules share some of the properties of PI -extending (i.e., every projection invariant submodule is ...
Kara Yeliz, Tercan Adnan
doaj   +1 more source

Generalization of p-Injective Rings and Projective Modules [PDF]

, 2013
Any left R-module M is said to be p-injective if for every principal left ideal I of R and any R-homomorphism g: I®M, there exists y ÎM such that  for all b in I.
Singh, D.S.
core   +1 more source

Closed ss-semilocal modules and rings

Open Mathematics
A module A is designated as closed ss -semilocal module provided for any closed submodule G of A, there exists a submodule H of A such that A = G + H and G ∩ H ≤ Soc s(A) where Soc s(A) = Rad(A) ∩ Soc(A) and a ring S is named as closed ss -semilocal ring
Önal Kır Emine
doaj   +1 more source

Classes of modules closed under projective covers

Open Mathematics
In this work, we study some classes of modules closed under submodules, quotients, and projective covers, even if the left projective cover of an arbitrary left module not always exists. We obtain a characterization of artinian principal ideal rings when
Cejudo-Castilla César, García-Ramírez Ángel Raúl, Montalvo Ivan Fernando Vilchis   +2 more
doaj   +1 more source

© Hindawi Publishing Corp. PROJECTIVITY AND FLATNESS OVER THE ENDOMORPHISM RING OF A FINITELY GENERATED MODULE

, 2003
Let A be a ring and Λ a finitely generated A-module. We give necessary and sufficient conditions for projectivity and flatness of a module over the endomorphism ring of Λ. 2000 Mathematics Subject Classification: 16D40, 16W30. 1.
S. Caenepeel, T. Guédénon
core  

On the relative homology of cleft extensions of rings and abelian categories

, 2000
We study the relative homological behaviour of the omnipresent class of cleft extensions of abelian categories. This class of extensions is a natural generalization of the trivial extensions studied in detail by Fossum, Griffith and Reiten and by Palmer ...
Beligiannis, A.
core