Shahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901ON COMULTIPLICATION AND R-MULTIPLICATION MODULES11929810.22044/jas.2014.298ENA. NiksereshtDepartment of Mathematics, Shiraz University, 71457-44776, Shiraz, Iran.H. SharifDepartment of Mathematics, Shiraz University, 71457-44776, Shiraz, Iran.Journal Article20131027We state several conditions under which comultiplication and weak comultiplication modules are cyclic and study strong comultiplication modules and comultiplication rings. In particular, we will show that every faithful weak comultiplication module having a maximal submodule 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].https://jas.shahroodut.ac.ir/article_298_f888f28d2d7511ee49e8903f7599a544.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901DIFFERENTIAL MULTIPLICATIVE HYPERRINGS213529910.22044/jas.2014.299ENL. Kamali ArdekaniDepartment of Mathematics, Yazd University, Yazd, Iran.B. DavvazDepartment of Mathematics, Yazd University, Yazd, Iran.https://orcid.org/00Journal 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.https://jas.shahroodut.ac.ir/article_299_420674ca212578f4903402930ff38459.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901A CHARACTERIZATION OF BAER-IDEALS375130010.22044/jas.2014.300ENA. TaherifarDepartment of Mathematics, Yasouj University, Yasouj, Iran.Journal Article20130903An ideal I of a ring R is called right Baer-ideal if there exists an idempotent e 2 R such that r(I) = eR. We know that R is quasi-Baer if every ideal of R 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 ideal of R is a right Baer-ideal. Therefore the concept of Baer ideal is important. In this paper we investigate some properties of Baer-ideals and give a characterization 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 equivalent conditions for which the 2-by-2 generalized triangular matrix ring is right <br />SA.https://jas.shahroodut.ac.ir/article_300_2e4cb45d9d8d73d64020a61a5b0b5a76.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901APPROXIMATE IDENTITY IN CLOSED CODIMENSION ONE IDEALS OF SEMIGROUP ALGEBRAS535930110.22044/jas.2014.301ENB. MohammadzadehDepartment of Mathematics, Babol University of Technology, Babol, Iran.Journal 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 bounded approximate identity in closed codimension one ideals of the semigroup algebra $M_a(S)$ of a locally compact topological foundation semigroup with identity.https://jas.shahroodut.ac.ir/article_301_7ee4ea8311e307d1890f997207da12dd.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901LIFTING MODULES WITH RESPECT TO A PRERADICAL616530210.22044/jas.2014.302ENT. AmouzegarDepartment of Mathematics, Quchan University of Advanced Technologies, Quchan,
Iran.Journal Article20130928Let $M$ be a right module over a ring $R$, $tau_M$ a preradical on $sigma[M]$, and $Ninsigma[M]$. In this note we show that if $N_1, N_2in sigma[M]$ are two $tau_M$-lifting modules such that $N_i$ is $N_j$-projective ($i,j=1,2$), then $N=N_1oplus N_2$ is $tau_M$-lifting. We investigate when homomorphic image of a $tau_M$-lifting module is $tau_M$-lifting.https://jas.shahroodut.ac.ir/article_302_b20995498df3389eed9b24a2342bd647.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901BEST APPROXIMATION IN QUASI TENSOR PRODUCT SPACE AND DIRECT SUM OF LATTICE NORMED SPACES678130310.22044/jas.2014.303ENM. IranmaneshDepartment of mathematical sciences, Shahrood university of technology, P.O.Box
3619995161-316, Shahrood, Iran.F. SolimaniDepartment of mathematical sciences, Shahrood university of technology, P.O.Box
3619995161-316, Shahrood, Iran.Journal Article20130518We study the theory of best approximation in tensor product and the direct sum of some lattice normed spaces<br />X_{i}. We introduce quasi tensor product space and discuss about the relation between tensor product space and this<br />new space which we denote it by X boxtimes Y. We investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downward or upward and we call them I_{m}-quasi downward or I_{m}-quasi upward.We show that these sets can be interpreted as downward or upward sets. The relation of these sets with<br />downward and upward subsets of the direct sum of lattice normed spaces X_{i} is discussed. This will be done by homomorphism functions. Finally, we introduce the best approximation of these sets.https://jas.shahroodut.ac.ir/article_303_47a2d4b1a718f29bd44bf701d6db4309.pdf