eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2014-09-01
2
1
1
19
10.22044/jas.2014.298
298
ON COMULTIPLICATION AND R-MULTIPLICATION MODULES
A. Nikseresht
a_nikseresht@shirazu.ac.ir
1
H. Sharif
sharif@susc.ac.ir
2
Department of Mathematics, Shiraz University, 71457-44776, Shiraz, Iran.
Department of Mathematics, Shiraz University, 71457-44776, Shiraz, Iran.
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].
http://jas.shahroodut.ac.ir/article_298_f888f28d2d7511ee49e8903f7599a544.pdf
Comultiplication Module
r-Multiplication Module
p-Comultiplication Module
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2014-09-01
2
1
21
35
10.22044/jas.2014.299
299
DIFFERENTIAL MULTIPLICATIVE HYPERRINGS
L. Kamali Ardekani
kamali_leili@yahoo.com
1
B. Davvaz
davvaz@yazd.ac.ir
2
Department of Mathematics, Yazd University, Yazd, Iran.
Department of Mathematics, Yazd University, Yazd, Iran.
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.
http://jas.shahroodut.ac.ir/article_299_420674ca212578f4903402930ff38459.pdf
multiplicative hyperring
derivation
differential hyperring
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2014-09-01
2
1
37
51
10.22044/jas.2014.300
300
A CHARACTERIZATION OF BAER-IDEALS
A. Taherifar
ataherifar54@gmail.com
1
Department of Mathematics, Yasouj University, Yasouj, Iran.
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.
http://jas.shahroodut.ac.ir/article_300_2e4cb45d9d8d73d64020a61a5b0b5a76.pdf
Quasi-Baer ring
Generalized right quasi-Baer
Semicentral idempotent
Spec(R)
Extremally disconnected space
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2014-09-01
2
1
53
59
10.22044/jas.2014.301
301
APPROXIMATE IDENTITY IN CLOSED CODIMENSION ONE IDEALS OF SEMIGROUP ALGEBRAS
B. Mohammadzadeh
b.mohammadzadeh@nit.ac.ir
1
Department of Mathematics, Babol University of Technology, Babol, Iran.
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.
http://jas.shahroodut.ac.ir/article_301_7ee4ea8311e307d1890f997207da12dd.pdf
Approximate identity
codimension one ideal
foundation semigroup
semigroup algebras
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2014-09-01
2
1
61
65
10.22044/jas.2014.302
302
LIFTING MODULES WITH RESPECT TO A PRERADICAL
T. Amouzegar
t.amoozegar@yahoo.com
1
Department of Mathematics, Quchan University of Advanced Technologies, Quchan, Iran.
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.
http://jas.shahroodut.ac.ir/article_302_b20995498df3389eed9b24a2342bd647.pdf
preradical
hereditary
$tau_M$-lifting module
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2014-09-01
2
1
67
81
10.22044/jas.2014.303
303
BEST APPROXIMATION IN QUASI TENSOR PRODUCT SPACE AND DIRECT SUM OF LATTICE NORMED SPACES
M. Iranmanesh
m.iranmanesh@shahroodut.ac.ir
1
F. Solimani
enfazh.bmaam@gmail.com
2
Department of mathematical sciences, Shahrood university of technology, P.O.Box 3619995161-316, Shahrood, Iran.
Department of mathematical sciences, Shahrood university of technology, P.O.Box 3619995161-316, Shahrood, Iran.
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.
http://jas.shahroodut.ac.ir/article_303_47a2d4b1a718f29bd44bf701d6db4309.pdf
Best approximation
proximinal set
downward set
tensor product
quasi tensor product