Abstract In this work we introduce the concept of approximately regular ring as generalizations of regular ring, and the sense of a Z- approximately regular module as generalizations of Z- regular module. We give many result about this concept.
In this paper, we study a new concept of fuzzy sub-module, called fuzzy socle semi-prime sub-module that is a generalization the concept of semi-prime fuzzy sub-module and fuzzy of approximately semi-prime sub-module in the ordinary sense. This leads us to introduce level property which studies the relation between the ordinary and fuzzy sense of approximately semi-prime sub-module. Also, some of its characteristics and notions such as the intersection, image and external direct sum of fuzzy socle semi-prime sub-modules are introduced. Furthermore, the relation between the fuzzy socle semi-prime sub-module and other types of fuzzy sub-module presented.
Let M be an R-module, where R is commutative ring with unity. In this paper we study the behavior of strongly hollow and quasi hollow submodule in the class of strongly comultiplication modules. Beside this we give the relationships between strongly hollow and quasi hollow submodules with V-coprime, coprime, bi-hollow submodules.
In this study, new heterocyclic compounds were synthesized through the cyclization reactions of o-phenylenediamine (1) with various organic reagents. Benzodiazepine derivatives (2-4) were obtained by reaction of (1) with ethylacetoacetate, malonic acid and acetyl acetone.Treatment of compound (1) with chloroacetamide, chloroacetic acid, p-bromophenacyl bromide and oxalic acid dihydrate afforded quinoxaline derivatives (5-8), respectively. Reaction of compound (1) with benzoic acid, piperonal, cyclohexanone and carbon disulfide resulted in the formation of compounds (9-12), respectively. Finally, reaction of compound (12) with chloroacetic acid in the presence of potassium hydroxide produced compound (13).
(1)
In this paper, we proved that if R is a prime ring, U be a nonzero Lie ideal of R , d be a nonzero (?,?)-derivation of R. Then if Ua?Z(R) (or aU?Z(R)) for a?R, then either or U is commutative Also, we assumed that Uis a ring to prove that: (i) If Ua?Z(R) (or aU?Z(R)) for a?R, then either a=0 or U is commutative. (ii) If ad(U)=0 (or d(U)a=0) for a?R, then either a=0 or U is commutative. (iii) If d is a homomorphism on U such that ad(U) ?Z(R)(or d(U)a?Z(R), then a=0 or U is commutative.
We present the concept of maps Γ- periodi2 on Γ -near-ring S. Our main goal is to research and explore the presence and mapping traits such as h Γ –hom anti-Γ –hom, Γ –α-derivations of Γ -periodi2 on Γ- near-rings.
New twin compounds having four-, five-, and seven- membered heterocyclic rings were synthesized via Schiff bases (1a,b) which were obtained by the condensation of o-tolidine with two moles of 4- N,N-dimethyl benzaldehyde or 4- chloro benzaldehyde. The reaction of these Schiff bases with two moles of phenyl isothiocyanate, phenyl isocyanate or naphthyl isocyanate as in scheme(1) led to the formation of bis -1,3- diazetidin- 2- thion and bis -1,3- diazetidin -2-one derivatives (2-4 a,b). While in scheme (2) bis imidazolidin-4-one (5a,b) ,bistetrazole (6a,b) and bis thiazolidin-4-one (7a,b) derivatives were produced by reacting the mentioned Schiff bases(1a,b)with two moles of glycine, sodium azide or thioglycolic acid, respectively. The new b
... Show MoreThe synthesis and properties of two new series of compounds having 1,3-Oxazepineand 1,3-thiazole rings connected through azo linkage are reported. These compounds weresynthesized by the reaction of phthalic anhydride with Schiff bases. The molecular structuresof these compounds were verified by elemental analysis, FTIR and 1HNMR spectroscopy.The mesomorphic behaviors of these compounds were studied by optical polarizedmicroscopy (OPM) and differential scanning calorimetry (DSC). All compounds of the twoseries show liquid crystalline properties. The influence of the central oxazepine and thiazolerings and the terminal substituents on the type and temperature range of the mesomorphousproperties of these compounds has been elucidated
The article presents the synthesis and liquid crystalline properties of some of new bent and linear core compounds containing a 1,3,4-oxadiazole, piperazine and thiazolidin-4-one rings as a central core. The new synthesized compounds were characterized by elemental analysis and FTIR, ¹HNMR and mass spectroscopy). The liquid crystalline properties were studied by polarized optical microscopy and differential scanning calorimetry. All Schiff bases compounds with 1,3,4-oxadiazole and piprzaine ring in central core presented liquid crystalline properties. The liquid crystallinity of compounds containing 1,3,4-oxadiazole and thiazolidin-4-one rings as a central core were found depending on the type of terminal substituents.