scholarly journals Direct products of modules whose endomorphism rings have at most two maximal ideals

2015 ◽  
Vol 435 ◽  
pp. 204-222
Author(s):  
Adel Alahmadi ◽  
Alberto Facchini
Keyword(s):  
Direct Products ◽  
Endomorphism Rings ◽  
Maximal Ideals

On a category of extensions whose endomorphism rings have at most four maximal ideals

2018 ◽  
pp. 107-126 ◽  
Author(s):  
Federico Campanini ◽  
Alberto Facchini
Keyword(s):  
Endomorphism Rings ◽  
Maximal Ideals

scholarly journals ON COHERENCE OF ENDOMORPHISM RINGS

2010 ◽  
Vol 81 (2) ◽  
pp. 186-194
Author(s):  
HAI-YAN ZHU ◽  
NAN-QING DING
Keyword(s):  
Direct Products ◽  
Endomorphism Rings ◽  
Coherent Ring

AbstractLet R be a ring and U a left R-module with S=End(RU). The aim of this paper is to characterize when S is coherent. We first show that a left R-module F is TU-flat if and only if HomR(U,F) is a flat left S-module. This removes the unnecessary hypothesis that U is Σ-quasiprojective from Proposition 2.7 of Gomez Pardo and Hernandez [‘Coherence of endomorphism rings’, Arch. Math. (Basel)48(1) (1987), 40–52]. Then it is shown that S is a right coherent ring if and only if all direct products of TU-flat left R-modules are TU-flat if and only if all direct products of copies of RU are TU-flat. Finally, we prove that every left R-module is TU-flat if and only if S is right coherent with wD(S)≤2 and US is FP-injective.

Central lifting property for orthomodular lattices

2020 ◽  
Vol 70 (6) ◽  
pp. 1307-1316
Author(s):  
Neda Arjomand Kermani ◽  
Esfandiar Eslami ◽  
Arsham Borumand Saeid
Keyword(s):  
Boolean Algebras ◽  
Prime Ideals ◽  
Direct Products ◽  
Orthomodular Lattices ◽  
Maximal Ideals ◽  
Central Elements ◽  
Simple Chain

AbstractWe introduce and investigate central lifting property (CLP) for orthomodular lattices as a property whereby all central elements can be lifted modulo every p-ideal. It is shown that prime ideals, maximal ideals and finite p-ideals have CLP. Also Boolean algebras, simple chain finite orthomodular lattices, subalgebras of an orthomodular lattices generated by two elements and finite orthomodular lattices have CLP. The main results of the present paper include the investigation of CLP for principal p-ideals and finite direct products of orthomodular lattices.

scholarly journals KERNELS OF MORPHISMS BETWEEN INDECOMPOSABLE INJECTIVE MODULES

2010 ◽  
Vol 52 (A) ◽  
pp. 69-82 ◽  
Author(s):  
ALBERTO FACCHINI ◽  
ŞULE ECEVIT ◽  
M. TAMER KOŞAN
Keyword(s):  
Local Ring ◽  
Endomorphism Ring ◽  
Weak Form ◽  
Indecomposable Module ◽  
Endomorphism Rings ◽  
Direct Sums ◽  
Indecomposable Modules ◽  
Direct Sum ◽  
Injective Modules ◽  
Maximal Ideals

AbstractWe show that the endomorphism rings of kernels ker ϕ of non-injective morphisms ϕ between indecomposable injective modules are either local or have two maximal ideals, the module ker ϕ is determined up to isomorphism by two invariants called monogeny class and upper part, and a weak form of the Krull–Schmidt theorem holds for direct sums of these kernels. We prove with an example that our pathological decompositions actually take place. We show that a direct sum ofnkernels of morphisms between injective indecomposable modules can have exactlyn! pairwise non-isomorphic direct-sum decompositions into kernels of morphisms of the same type. IfERis an injective indecomposable module andSis its endomorphism ring, the duality Hom(−,ER) transforms kernels of morphismsER→ERinto cyclically presented left modules over the local ringS, sending the monogeny class into the epigeny class and the upper part into the lower part.

scholarly journals Finitary ideals of direct products in quantales

2021 ◽  
Vol 3 (1) ◽  
pp. 23-28
Author(s):  
Pascal Pankiti ◽  
C Nkuimi-Jugnia
Keyword(s):  
Complete Lattice ◽  
Tensor Category ◽  
Prime Ideals ◽  
Direct Products ◽  
C Algebra ◽  
Maximal Ideals ◽  
The Common ◽  
Radical Ideals ◽  
Primary Ideals ◽  
Unital Rings

The notion of quantale, which designates a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins, appears in various areasof mathematics-in quantaloid theory, in non classical logic as completion of the Lindebaum algebra, and in different representations of the spectrum of a C∗ algebra asmany-valued and non commutative topologies. To put it briefly, its importance is nolonger to be demonstrated. Quantales are ring-like structures in that they share withrings the common fact that while as rings are semi groups in the tensor category ofabelian groups, so quantales are semi groups in the tensor category of sup-lattices.In 2008 Anderson and Kintzinger [1] investigated the ideals, prime ideals, radical ideals, primary ideals, and maximal of a product ring R × S of two commutativenon non necceray unital rings R and S: Something resembling rings are quantales byanalogy with what is studied in ring, we begin an investigation on ideals of a productof two quantales. In this paper, given two quantales Q1 and Q2; not necessarily withidentity, we investigate the ideals, prime ideals, primary ideals, and maximal ideals ofthe quantale Q1 × Q2

scholarly journals IDEALS IN DIRECT PRODUCTS OF COMMUTATIVE RINGS

2008 ◽  
Vol 77 (3) ◽  
pp. 477-483
Author(s):  
D. D. ANDERSON ◽  
JOHN KINTZINGER
Keyword(s):  
Abelian Group ◽  
Maximal Ideal ◽  
Commutative Rings ◽  
Primary Ideal ◽  
Maximal Subgroups ◽  
Prime Ideals ◽  
Direct Products ◽  
Maximal Ideals ◽  
Radical Ideals ◽  
Primary Ideals

AbstractLet R and S be commutative rings, not necessarily with identity. We investigate the ideals, prime ideals, radical ideals, primary ideals, and maximal ideals of R×S. Unlike the case where R and S have an identity, an ideal (or primary ideal, or maximal ideal) of R×S need not be a ‘subproduct’ I×J of ideals. We show that for a ring R, for each commutative ring S every ideal (or primary ideal, or maximal ideal) is a subproduct if and only if R is an e-ring (that is, for r∈R, there exists er∈R with err=r) (or u-ring (that is, for each proper ideal A of R, $\sqrt {A}\not =R$)), the Abelian group (R/R2 ,+) has no maximal subgroups).

scholarly journals Endomorphism Rings Via Minimal Morphisms

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Manuel Cortés-Izurdiaga ◽  
Pedro A. Guil Asensio ◽  
D. Keskin Tütüncü ◽  
Ashish K. Srivastava
Keyword(s):  
Endomorphism Rings

On the computation of the endomorphism rings of abelian surfaces

2021 ◽  
Author(s):  
Claus Fieker ◽  
Tommy Hofmann ◽  
Sogo Pierre Sanon
Keyword(s):  
Abelian Surfaces ◽  
Endomorphism Rings

Generators of infinite direct products of unitary groups

1977 ◽  
Vol 18 (11) ◽  
pp. 2166-2171 ◽  
Author(s):  
K. Kraus ◽  
L. Polley ◽  
G. Reents
Keyword(s):  
Unitary Groups ◽  
Direct Products
Sign in / Sign up

Export Citation Format

Share Document