Correction to: On S-multiplication modules
نویسندگان
چکیده
منابع مشابه
ON COMULTIPLICATION AND R-MULTIPLICATION MODULES
We state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. In particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. Also we show that if M is an strong comultiplicati...
متن کاملOn Multiplication Modules
Let R be a commutative ring with identity and M be a unital R-module. Then M is called a multiplication module provided for every submodule N of M there exists an ideal I of R such that N = IM. Our objective is to investigate properties of prime and semiprime submodules of multiplication modules. Mathematics Subject Classification: 13C05, 13C13
متن کاملThe small intersection graph relative to multiplication modules
Let $R$ be a commutative ring and let $M$ be an $R$-module. We define the small intersection graph $G(M)$ of $M$ with all non-small proper submodules of $M$ as vertices and two distinct vertices $N, K$ are adjacent if and only if $Ncap K$ is a non-small submodule of $M$. In this article, we investigate the interplay between the graph-theoretic properties of $G(M)$ and algebraic properties of $M...
متن کاملMultiplication operators on Banach modules over spectrally separable algebras
Let $mathcal{A}$ be a commutative Banach algebra and $mathscr{X}$ be a left Banach $mathcal{A}$-module. We study the set ${rm Dec}_{mathcal{A}}(mathscr{X})$ of all elements in $mathcal{A}$ which induce a decomposable multiplication operator on $mathscr{X}$. In the case $mathscr{X}=mathcal{A}$, ${rm Dec}_{mathcal{A}}(mathcal{A})$ is the well-known Apostol algebra of $mathcal{A}$. We s...
متن کاملSome remarks on multiplication modules
In this note all rings are commutat ive rings with identity and all modules are unital. Let R be a commutat ive ring with identity. An R-module M is called a mult ipl icat ion module provided for each submodule N of M there exists an ideal I of R such that N = I M. Various propert ies of mult ipl icat ion modules are considered. If there is a common theme it is that the methods used generalise ...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2021
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2021.1873356