SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS

نویسنده

  • M. Ebrahimpour Department of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan , P.O.Box 518, Rafsanjan, Iran
چکیده مقاله:

Let R be a commutative ring with identity and Mbe a unitary R-module. In this paper we generalize the conceptmultiplicatively closed subset of R and we study some propertiesof these genaralized subsets of M. Among the many results in thispaper, we generalize some well-known theorems about multiplicativelyclosed subsets of R to these generalized subsets of M. Alsowe show that some other well-known results about multiplicativelyclosed subsets of R are not valid for these generalized subsets ofM.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Some remarks on generalizations of classical prime submodules

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. Suppose that $phi:S(M)rightarrow S(M)cup lbraceemptysetrbrace$ be a function where $S(M)$ is the set of all submodules of $M$. A proper submodule $N$ of $M$ is called an $(n-1, n)$-$phi$-classical prime submodule, if whenever $r_{1},ldots,r_{n-1}in R$ and $min M$ with $r_{1}ldots r_{n-1}min Nsetminusphi(N)$, then $r_{1...

متن کامل

Some Generalizations of Locally Closed Sets

Arenas et al. [1] introduced the notion of lambda-closed sets as a generalization of locally closed sets. In this paper, we introduce the notions of lambda-locally closed sets, Lambda_lambda-closed sets and lambda_g-closed sets and obtain some decompositions of closed sets and continuity in topological spaces.

متن کامل

Inert Module Extensions, Multiplicatively Closed Subsets Conserving Cyclic Submodules and Factorization in Modules

Introduction Suppose that  is a commutative ring with identity,  is a unitary -module and  is a multiplicatively closed subset of .  Factorization theory in commutative rings, which has a long history, still gets the attention of many researchers. Although at first, the focus of this theory was factorization properties of elements in integral domains, in the late nineties the theory was gener...

متن کامل

Generalizations of Product-Free Subsets

In this paper, we present some generalizations of Gowers’s result about product-free subsets of groups. For any group G of order n, a subset A of G is said to be product-free if there is no solution of the equation ab = c with a, b, c ∈ A. Previous results showed that the size of any product-free subset of G is at most n/δ1/3, where δ is the smallest dimension of a nontrivial representation of ...

متن کامل

Some Remarks on Roeper’s Remarks on Chomsky’s ‘Remarks’

In his 1970 paper ‘Remarks on nominalization’, Noam Chomsky provided several arguments for the lexicalist hypothesis, namely the idea that nouns like refusal, rejection, growth, and so on are nouns throughout the entire syntactic derivation. Tom Roeper’s paper ‘Chomsky’s Remarks and the transformationalist hypothesis’ challenges the lexicalist hypothesis, arguing that such nouns are syntactical...

متن کامل

Some remarks on the arithmetic-geometric index

Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.

متن کامل

منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ذخیره در منابع من قبلا به منابع من ذحیره شده

{@ msg_add @}


عنوان ژورنال

دوره 4  شماره 1

صفحات  15- 27

تاریخ انتشار 2016-09-01

با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023