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.
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.
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.
Throughout this paper we introduce the concept of quasi closed submodules which is weaker than the concept of closed submodules. By using this concept we define the class of fully extending modules, where an R-module M is called fully extending if every quasi closed submodule of M is a direct summand.This class of modules is stronger than the class of extending modules. Many results about this concept are given, also many relationships with other related concepts are introduced.
Let R be a commutative ring with identity, and let M be a unity R-module. M is called a bounded R-module provided that there exists an element x?M such that annR(M) = annR(x). As a generalization of this concept, a concept of semi-bounded module has been introduced as follows: M is called a semi-bounded if there exists an element x?M such that . In this paper, some properties and characterizations of semi-bounded modules are given. Also, various basic results about semi-bounded modules are considered. Moreover, some relations between semi-bounded modules and other types of modules are considered.
To determine the potential of gingival crevicular fluid (GCF) volume, E‐cadherin and total antioxidant capacity (TAC) levels to predict the outcomes of nonsurgical periodontal therapy (NSPT) for periodontitis patients.
NSPT is the gold‐standard treatment for periodontal pockets < 6 mm in depth, however, successful outcomes are not always guaranteed due to several factors. Periodontitis‐associated tissue destruction is evidenced by the increased level of soluble E‐cadherin and reduced antioxidants in oral fluids which could be used as predictors for success/failure of N
A histological study showed the wall of the stomach in Pica pica and Herpestes javanicus consists of four layers: mucosa, submucosa, muscularis externa and serosa. Also, the present study showed many differences in the histological structures of the stomach for each in both types. The stomach of P. pica consists of two portions: the proventiculus and gizzard, while the stomach of H. javanicus consists of three portions: cardiac, fundic and pyloric regions. The mucosa layer formed short gastric folds, named plicae. In the proventiculus of P. pica, sulcus is found between each two plicae, but the folds called gastric p
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