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St-Closed and Semi-extending Modules
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Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of M is called St-closed in M, if N has no proper semi-essential extension in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K, then N = K. We investigate the main properties of this type of submodules, and discuss some results that are useful in our work. The class of semi-extending modules is a generalization to the notion of extending modules, where an R-module M is called semi-extending, if every submodule of M is a semi-essential in a direct summand of M. Various properties of semi-extending modules are obtained, and we study the relationships between this class of modules and other related concepts.

Publication Date
Sat May 01 2021
Journal Name
Journal Of Physics: Conference Series
On semi strongly (E, F)-convex functions and semi strongly (E, F)-convex optimization problems
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Abstract<p>In this paper, a new class of non-convex functions called semi strongly (<italic>E, F</italic>)-convex functions are presented. This class represents a natural extension of semi strongly <italic>E</italic>-convex functions shown in the literature. Different properties of this class of functions are discussed. Optimality properties of constrained optimization problems in which the objective function or the inequality constraints functions are semi strongly (<italic>E, F</italic>)-convex are proved for this class.</p>
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Publication Date
Sun Dec 04 2011
Journal Name
Baghdad Science Journal
Approximate Regular Modules
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There are two (non-equivalent) generalizations of Von Neuman regular rings to modules; one in the sense of Zelmanowize which is elementwise generalization, and the other in the sense of Fieldhowse. In this work, we introduced and studied the approximately regular modules, as well as many properties and characterizations are considered, also we study the relation between them by using approximately pointwise-projective modules.

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Publication Date
Tue Jan 01 2002
Journal Name
Iraqi Journal Of Science
On Regular Modules
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Let R be a commutative ring with identity, and let M be a unitary left R-module. M is called Z-regular if every cyclic submodule (equivalently every finitely generated) is projective and direct summand. And a module M is F-regular if every submodule of M is pure. In this paper we study a class of modules lies between Z-regular and F-regular module, we call these modules regular modules.

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Publication Date
Sun May 01 2022
Journal Name
Journal Of Physics: Conference Series
D_j -Supplemented Modules
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Publication Date
Fri Jan 01 2010
Journal Name
Iraqi Journal Of Science
PRIME HOLLOW MODULES
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A non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting modules.

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Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
⊕-Rad -supplemented modules
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Publication Date
Thu Oct 16 2014
Journal Name
Journal Of Advances In Mathematics
Strongly Rickart Modules
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Publication Date
Tue Jan 01 2002
Journal Name
Iraqi Journal Of Science
Special selfgenerator Modules
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Let R be a commutative ring with identity, and let M be a unitary left R-module. M is called special selfgenerator or weak multiplication module if for each cyclic submodule Ra of M (equivalently, for each submodule N of M) there exists a family {fi} of endomorphism of M such that Ra = ∑_i▒f_i (M) (equivalently N = ∑_i▒f_i (M)). In this paper we introduce a class of modules properly contained in selfgenerator modules called special selfgenerator modules, and we study some of properties of these modules.

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Publication Date
Fri May 01 2020
Journal Name
Journal Of Physics: Conference Series
⊕-J-supplemented modules
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Publication Date
Sun Sep 03 2017
Journal Name
Baghdad Science Journal
CL-duo modules
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In this paper, we introduce and study a new concept (up to our knowledge) named CL-duo modules, which is bigger than that of duo modules, and smaller than weak duo module which is given by Ozcan and Harmanci. Several properties are investigated. Also we consider some characterizations of CL-duo modules. Moreover, many relationships are given for this class of modules with other related classes of modules such as weak duo modules, P-duo modules.

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