Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2
1
2014
09
01
ON COMULTIPLICATION AND R-MULTIPLICATION MODULES
1
19
EN
A.
Nikseresht
Department of Mathematics, Shiraz University, 71457-44776, Shiraz, Iran.
a_nikseresht@shirazu.ac.ir
H.
Sharif
Department of Mathematics, Shiraz University, 71457-44776, Shiraz, Iran.
sharif@susc.ac.ir
10.22044/jas.2014.298
We 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].
Comultiplication Module,r-Multiplication Module,p-Comultiplication Module
http://jas.shahroodut.ac.ir/article_298.html
http://jas.shahroodut.ac.ir/article_298_f888f28d2d7511ee49e8903f7599a544.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2
1
2014
09
01
DIFFERENTIAL MULTIPLICATIVE HYPERRINGS
21
35
EN
L.
Kamali Ardekani
Department of Mathematics, Yazd University, Yazd, Iran.
kamali_leili@yahoo.com
B.
Davvaz
Department of Mathematics, Yazd University, Yazd, Iran.
davvaz@yazd.ac.ir
10.22044/jas.2014.299
There 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.
multiplicative hyperring,derivation,differential hyperring
http://jas.shahroodut.ac.ir/article_299.html
http://jas.shahroodut.ac.ir/article_299_420674ca212578f4903402930ff38459.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2
1
2014
09
01
A CHARACTERIZATION OF BAER-IDEALS
37
51
EN
A.
Taherifar
Department of Mathematics, Yasouj University, Yasouj, Iran.
ataherifar54@gmail.com
10.22044/jas.2014.300
An 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.
Quasi-Baer ring,Generalized right quasi-Baer,Semicentral idempotent,Spec(R),Extremally disconnected space
http://jas.shahroodut.ac.ir/article_300.html
http://jas.shahroodut.ac.ir/article_300_2e4cb45d9d8d73d64020a61a5b0b5a76.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2
1
2014
09
01
APPROXIMATE IDENTITY IN CLOSED CODIMENSION ONE IDEALS OF SEMIGROUP ALGEBRAS
53
59
EN
B.
Mohammadzadeh
Department of Mathematics, Babol University of Technology, Babol, Iran.
b.mohammadzadeh@nit.ac.ir
10.22044/jas.2014.301
Let 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.
Approximate identity,codimension one ideal,foundation semigroup,semigroup algebras
http://jas.shahroodut.ac.ir/article_301.html
http://jas.shahroodut.ac.ir/article_301_7ee4ea8311e307d1890f997207da12dd.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2
1
2014
09
01
LIFTING MODULES WITH RESPECT TO A PRERADICAL
61
65
EN
T.
Amouzegar
Department of Mathematics, Quchan University of Advanced Technologies, Quchan,
Iran.
t.amoozegar@yahoo.com
10.22044/jas.2014.302
Let $M$ 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.
preradical,hereditary,$tau_M$-lifting module
http://jas.shahroodut.ac.ir/article_302.html
http://jas.shahroodut.ac.ir/article_302_b20995498df3389eed9b24a2342bd647.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2
1
2014
09
01
BEST APPROXIMATION IN QUASI TENSOR PRODUCT SPACE AND DIRECT SUM OF LATTICE NORMED SPACES
67
81
EN
M.
Iranmanesh
Department of mathematical sciences, Shahrood university of technology, P.O.Box
3619995161-316, Shahrood, Iran.
m.iranmanesh@shahroodut.ac.ir
F.
Solimani
Department of mathematical sciences, Shahrood university of technology, P.O.Box
3619995161-316, Shahrood, Iran.
enfazh.bmaam@gmail.com
10.22044/jas.2014.303
We 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.
Best approximation,proximinal set,downward set,tensor product,quasi tensor product
http://jas.shahroodut.ac.ir/article_303.html
http://jas.shahroodut.ac.ir/article_303_47a2d4b1a718f29bd44bf701d6db4309.pdf