Preferred Language
Articles
/
Lxfi4I0BVTCNdQwCkijk
Epiform∗ Modules

Let R be a commutative ring with unity 1 6= 0, and let M be a unitary left module over R. In this paper we introduce the notion of epiform∗ modules. Various properties of this class of modules are given and some relationships between these modules and other related modules are introduced.

View Publication
Publication Date
Mon Aug 26 2019
Journal Name
Iraqi Journal Of Science
On Weakly Second Submodules

    Let  be a non-zero right module over a ring  with identity. The weakly second submodules is studied in this paper. A non-zero submodule  of   is weakly second Submodule when  ,  where ,  and  is a submodule of  implies either  or   . Some connections between these modules and other related modules are investigated and number of conclusions  and characterizations are gained.

View Publication Preview PDF
Scopus Crossref
Publication Date
Sun Oct 27 2019
Journal Name
Iraqi Journal Of Science
I-Nearly Primary Submodules

View Publication Preview PDF
Scopus Crossref
Publication Date
Wed Nov 27 2019
Journal Name
Iraqi Journal Of Science
I-Nearly Prime Submodules

     Let  be a commutative ring with identity, and a fixed ideal of  and  be an unitary -module. In this paper we  introduce and study the concept of -nearly prime submodules as genrealizations of nearly prime and we investigate some properties of this class of submodules. Also, some characterizations of -nearly prime submodules will be given.

View Publication Preview PDF
Scopus (7)
Crossref (4)
Scopus Crossref
Publication Date
Mon Jan 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Pseudo Weakly Closed Submodules and Related Concepts

Let  be a commutative ring with identity, and  be a unitary left -module. In this paper we introduce the concept pseudo weakly closed submodule as a generalization of -closed submodules, where a submodule  of an -module  is called a pseudo weakly closed submodule, if for all , there exists a -closed submodule  of  with  is a submodule of  such that . Several basic properties, examples and results of pseudo weakly closed submodules are given. Furthermore the behavior of pseudo weakly closed submodules in class of multiplication modules are studied. On the other hand modules with chain conditions on pseudo weakly closed submodules are established. Also, the relationships of  pseudo weakly closed

... Show More
View Publication Preview PDF
Crossref
Publication Date
Sat Apr 30 2022
Journal Name
Iraqi Journal Of Science
On Quasi-Small Prime Submodules

     Let  be a commutative  ring with identity , and  be a unitary (left) R-module. A proper submodule  of  is said to be quasi- small prime submodule  , if whenever   with  and , then either or . In this paper ,we give a comprehensive study of quasi- small prime submodules.

View Publication Preview PDF
Scopus (2)
Crossref (1)
Scopus Crossref
Publication Date
Mon May 28 2018
Journal Name
Iraqi Journal Of Science
On Essential (Complement) Submodules with Respect to an Arbitrary Submodule

 

View Publication Preview PDF
Publication Date
Thu Jul 01 2021
Journal Name
Iraqi Journal Of Science
Semi -T- Small Submodules

Let  be a ring with identity and  be a submodule of a left - module . A submodule  of  is called - small in  denoted by , in case for any submodule  of ,  implies .  Submodule  of  is called semi -T- small in , denoted by , provided for submodule  of ,  implies that . We studied this concept which is a generalization of the small submodules and obtained some related results

View Publication Preview PDF
Scopus (3)
Scopus Crossref
Publication Date
Mon May 20 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Pseudo Quasi-2-Absorbing Submodules and Some Related Concepts

Let R be a ring and let A be a unitary left R-module. A proper submodule H of an R-module A is called 2-absorbing , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H or rs∈[H:A], and a proper submodule H of an R-module A is called quasi-prime , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H. This led us to introduce the concept pseudo quasi-2-absorbing submodule, as a generalization of both concepts above, where a proper submodule H of an R-module A is called a pseudo quasi-2-absorbing submodule of A, if whenever rsta∈H,where r,s,t∈R,a∈A, implies that either rsa∈H+soc(A) or sta∈H+soc(A) or rta∈H+soc(A), where soc(A) is socal of an

... Show More
View Publication Preview PDF
Crossref (1)
Crossref
Publication Date
Mon May 20 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Approximaitly Prime Submodules and Some Related Concepts

In this research note approximately prime submodules is defined as a new generalization of prime submodules of unitary modules over a commutative ring with identity. A proper submodule  of an -module  is called an approximaitly prime submodule of  (for short app-prime submodule), if when ever , where , , implies that either  or . So, an ideal  of a ring  is called app-prime ideal of  if   is an app-prime submodule of -module . Several basic properties, characterizations and examples of approximaitly prime submodules were given. Furthermore, the definition of approximaitly prime radical of submodules of modules were introduced, and some of it is properties were established.

View Publication Preview PDF
Crossref (3)
Crossref
Publication Date
Thu Dec 02 2021
Journal Name
Iraqi Journal Of Science
Equality of Dedekind sums modulo 72Z

According to the wide appearance of Dedekind sums in different applications on different subjects, a new approach for the equivalence of the essential and sufficient condition for ( ) ( ) in and ( ) ( ) in where ( ) Σ(( ))(( )) and the equality of .two .Dedekind sums with their connections is given. The conditions for ( ) ( ) in which is equivalent to ( )– ( ) in were demonstrated with condition that of does not divide . Some applications for the important of Dedekind sums were given.

View Publication