Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.
The aim of this paper is to introduce the definition of projective 3-space over Galois field GF(q), q = pm, for some prime number p and some integer m.
Also the definitions of (k,n)-arcs, complete arcs, n-secants, the index of the point and the projectively equivalent arcs are given.
Moreover some theorems about these notations are proved.
Let R be a commutative ring with identity and M an unitary R-module. Let ï¤(M) be the set of all submodules of M, and ï¹: ï¤(M)  ï¤(M)  {ï¦} be a function. We say that a proper submodule P of M is end-ï¹-prime if for each ï¡ ïƒŽ EndR(M) and x  M, if ï¡(x)  P, then either x  P + ï¹(P) or ï¡(M) ïƒ P + ï¹(P). Some of the properties of this concept will be investigated. Some characterizations of end-ï¹-prime submodules will be given, and we show that under some assumtions prime submodules and end-ï¹-prime submodules are coincide.
Nowadays, the use of medicinal plants is being practiced at a wide range as a result of antibiotics resistant for the vast majority of microorganisms. Eucalyptus camaldulensis essential oil and hydrosol were used in this study against planktonic forms and biofilms of some species of Gram negative and Gram positive bacteria. The antibacterial and antibiofilm activities of this plant were detected using the microtiter plate and MIC approaches. The results proposed that the oil and hydrosol preparations have antibacterial activities against planktonic cells in different concentrations depending on the type of isolate. For antibiofilm activity, the results showed that E. camaldulensis oil was highly effective against bacter
... Show MoreDubas bug, Ommatissus lybicus (Asche and Wilson) is one of the major sucking pests of date palm. Both nymphs causes severe damage to the leaves by sucking the cell sap . If the damage is severe, it could cause the death of the date palms. The effect of different concentrations of some natural plant essential oils was evaluated on fifth instar nymphs of the insect. The results clearly demonstrated that the tested oils from mint (Mentha piperata), Parsley (Petroselinum sativum), Clove (Syzygium aromaticum), and Eucalyptus (Eucalyptus globules) to evaluate their effect on fecundity of fertile female resulted from these exposed instars nymphs and hatching of these egg. The corrected mortality and numbers of eggs laid, hatching, were studied.
... Show MoreLet 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.
Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if
the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are introduced and given some properties .
In this paper, we introduce the concept of a quasi-radical semi prime submodule. Throughout this work, we assume that is a commutative ring with identity and is a left unitary R- module. A proper submodule of is called a quasi-radical semi prime submodule (for short Q-rad-semiprime), if for , ,and then . Where is the intersection of all prime submodules of .
In this paper, the concept of normalized duality mapping has introduced in real convex modular spaces. Then, some of its properties have shown which allow dealing with results related to the concept of uniformly smooth convex real modular spaces. For multivalued mappings defined on these spaces, the convergence of a two-step type iterative sequence to a fixed point is proved
This study aimed to evaluate good manufacturing practices in food safety of ten different restaurants in the Al-Karkh area of Baghdad, Iraq. Forty samples collected from were collected from knives, food cutting boards, tables, hands and nails workers in restaurants. In addition. 70 food handlers were selected. Through structured interviews, information on the checklist for Good Manufacturing Practices in Food Safety, Food handlers’ general checklist for good hygiene, and Personal Hygiene Checklist were collected. The overall viable bacterial count before Good Hygiene Practices was significantly higher (P<0.05) than the total bacterial counts after Good Hygiene Practices. The highest viable bacterial counts before Good Hygiene P
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