Let R be a commutative ring with unity and let M be an R-module. In this paper we
study strongly (completely) hollow submodules and quasi-hollow submodules. We investigate
the basic properties of these submodules and the relationships between them. Also we study
the be behavior of these submodules under certain class of modules such as compultiplication,
distributive, multiplication and scalar modules. In part II we shall continue the study of these
submodules.
In this work we discuss the concept of pure-maximal denoted by (Pr-maximal) submodules as a generalization to the type of R- maximal submodule, where a proper submodule of an R-module is called Pr- maximal if ,for any submodule of W is a pure submodule of W, We offer some properties of a Pr-maximal submodules, and we give Definition of the concept, near-maximal, a proper submodule
of an R-module is named near (N-maximal) whensoever is pure submodule of such that then K=.Al so we offer the concept Pr-module, An R-module W is named Pr-module, if every proper submodule of is Pr-maximal. A ring is named Pr-ring if whole proper ideal of is a Pr-maximal ideal, we offer the concept pure local (Pr-loc
... Show MoreThe goal of this research is to introduce the concepts of Large-coessential submodule and Large-coclosed submodule, for which some properties are also considered. Let M be an R-module and K, N are submodules of M such that , then K is said to be Large-coessential submodule, if . A submodule N of M is called Large-coclosed submodule, if K is Large-coessential submodule of N in M, for some submodule K of N, implies that .
PPSU hollow fiber nanofiltration membranes are prepared by applying two concentrations and various extrusion pressures according to the phase inversion method. Cross-sectional area and outer structures were characterized by using scanning electron microscope (SEM) and atomic force microscopy (AFM). In additional to the pore size distribution, either the mean roughness or the mean pore size of the PPSU hollow fiber surfaces was evaluated by AFM. It was found that the morphology of the PPSU fibers had both sponge-like and finger-like structures through different extrusion pressures and PPSU concentrations. The mean pore size and mean roughness for inner and outer surfaces were seen to be decreased with the increase of extrusion pressure at
... Show MoreThe association of phytoplasma was investigated in symptomatic tomato (
An abortion that occurs spontaneously is known as a miscarriage. Various effectors associated with abortion such as Genetic and uterine anomalies, Endocrinopathy, immunological dysfunctions, infectious agents, environmental contaminants, psychogenetic elements, and endometriosis. Maternal infections considered the main reason for pregnancy wastage in females with Bad Obstetric History (BOH). Candida albicans is a dimorphic fungus that can grow as yeast or filamentous cells and considered one of the limited species of the Candida genus that cause humans candidiasis. It is an opportunistic fungus that responsible for mucosal infections in the mouth and genital tract. Excessive growth of C. albicans will follow with Vulvovaginal candid
... Show MoreThe goal of this research is to introduce the concepts of Large-small submodule and Large-hollow module and some properties of them are considered, such that a proper submodule N of an R-module M is said to be Large-small submodule, if N + K = M where K be a submodule of M, then K is essential submodule of M ( K ≤e M ). An R-module M is called Large-hollow module if every proper submodule of M is Large-small submodule in M.
Suppose R has been an identity-preserving commutative ring, and suppose V has been a legitimate submodule of R-module W. A submodule V has been J-Prime Occasionally as well as occasionally based on what’s needed, it has been acceptable: x ∈ V + J(W) according to some of that r ∈ R, x ∈ W and J(W) an interpretation of the Jacobson radical of W, which x ∈ V or r ∈ [V: W] = {s ∈ R; sW ⊆ V}. To that end, we investigate the notion of J-Prime submodules and characterize some of the attributes of has been classification of submodules.