Shahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901ON COMULTIPLICATION AND R-MULTIPLICATION MODULES11929810.22044/jas.2014.298ENAshkan NiksereshtShiraz UniversityHabib SharifShiraz UniversityJournal Article20131027We state several conditions under which comultiplication and weak comultiplication modules<br />are cyclic and study strong comultiplication modules and comultiplication rings. In particular,<br />we will show that every faithful weak comultiplication module having a maximal submodule<br />over a reduced ring with a finite indecomposable decomposition is cyclic. Also we show that if M is an strong comultiplication R-module, then R is semilocal and M is finitely cogenerated.<br />Furthermore, we define an R-module M to be p-comultiplication, if every nontrivial submodule of M is the annihilator of some prime ideal of R containing the annihilator of M and give a characterization of all cyclic p-comultiplication modules. Moreover, we prove that every pcomultiplication module which is not cyclic, has no maximal submodule and its annihilator is not prime. Also we give an example of a module over a Dedekind domain which is not weak comultiplication, but all of whose localizations at prime ideals are comultiplication and hence serves as a counterexample to [10, Proposition 2.3] and [11, Proposition 2.4].Shahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901DIFFERENTIAL MULTIPLICATIVE HYPERRINGS213529910.22044/jas.2014.299ENL. Kamali ArdekaniYazd UniversityBijan DavvazYazd UniversityJournal Article20130621There are several kinds of hyperrings, for example, Krasner<br />hyperrings, multiplicative hyperring, general hyperrings and<br />$H_v$-rings. In a multiplicative hyperring, the multiplication is<br />a hyperoperation, while the addition is a binary operation.<br /> In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. <br />{bf Keywords:} multiplicative hyperring, derivation, differential hyperring.Shahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901A CHARACTERIZATION OF BAER-IDEALS375130010.22044/jas.2014.300ENAli TaherifarYasouj UniversityJournal Article20130903An ideal I of a ring R is called right Baer-ideal if there exists an idempotent <br />e 2 R such that r(I) = eR. We know that R is quasi-Baer if every ideal of R <br />is a right Baer-ideal, R is n-generalized right quasi-Baer if for each I E R the ideal <br />In is right Baer-ideal, and R is right principaly quasi-Baer if every principal right <br />ideal of R is a right Baer-ideal. Therefore the concept of Baer ideal is important. In <br />this paper we investigate some properties of Baer-ideals and give a characterization <br />of Baer-ideals in 2-by-2 generalized triangular matrix rings, full and upper triangular <br />matrix rings, semiprime ring and ring of continuous functions. Finally, we find <br />equivalent conditions for which the 2-by-2 generalized triangular matrix ring is right <br />SA.Shahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901APPROXIMATE IDENTITY IN CLOSED CODIMENSION ONE IDEALS OF SEMIGROUP ALGEBRAS535930110.22044/jas.2014.301ENbharam MohammadzadehBabol university of technology- Babol IranJournal Article20130717Let S be a locally compact topological foundation semigroup with identity and Ma(S) be its semigroup algebra. In this paper, we give necessary and sufficient conditions to have a<br />bounded approximate identity in closed codimension one ideals of the semigroup algebra $M_a(S)$ of a locally compact topological foundation<br />semigroup with identity.Shahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901LIFTING MODULES WITH RESPECT TO A PRERADICAL616530210.22044/jas.2014.302ENTayyebeh AmouzegarDepartment of Mathematics,
Quchan Institute of Engineering
and Technology, Quchan, IranJournal Article20130928Let $M$ be a right module over a ring $R$, $tau_M$ a preradical on $sigma[M]$, and<br />$Ninsigma[M]$. In this note we show that if $N_1, N_2in sigma[M]$ are two<br />$tau_M$-lifting modules such that $N_i$ is $N_j$-projective ($i,j=1,2$), then $N=N_1oplus<br />N_2$ is $tau_M$-lifting. We investigate when homomorphic image of a $tau_M$-lifting module<br />is $tau_M$-lifting.Shahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901BEST APPROXIMATION IN QUASI TENSOR PRODUCT SPACE AND DIRECT SUM OF LATTICE NORMED SPACES678130310.22044/jas.2014.303ENMahdi IranmaneshDepartment of Mathematics,.Shahrood University of Tecnology, Shahrood, Iran. P.O.BOX 3619995161-316Fateme SolimaniDepartment of mathematical sciences, Shahrood university of technologyJournal Article20130518We study the theory of best approximation in tensor product <br />and the direct sum of some lattice normed spaces<br />X_{i}. We introduce quasi tensor product space and<br />discuss about the relation between tensor product space and this<br />new space which we denote it by X boxtimes<br />Y. We investigate best approximation in<br /> direct sum of lattice normed spaces by elements<br /> which are not necessarily downward<br />or upward and we call them I_{m}-quasi downward or I_{m}-quasi upward.<br />We show that these sets can be interpreted as downward<br /> or upward sets. The relation of these sets with<br />downward and upward subsets of the direct sum of lattice normed<br />spaces X_{i} is discussed. This will be done by homomorphism<br />functions. Finally, we introduce the best approximation of these<br />sets.