2014
2
1
1
81
ON COMULTIPLICATION AND RMULTIPLICATION MODULES
2
2
We state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. In particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. Also we show that if M is an strong comultiplication Rmodule, then R is semilocal and M is finitely cogenerated.Furthermore, we define an Rmodule M to be pcomultiplication, 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 pcomultiplication 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].
1

1
19


Ashkan
Nikseresht
Shiraz University
Shiraz University
Iran
a_nikseresht@shirazu.ac.ir


Habib
Sharif
Shiraz University
Shiraz University
Iran
sharif@susc.ac.ir
Comultiplication Module
rMultiplication Module
pComultiplication Module
DIFFERENTIAL MULTIPLICATIVE HYPERRINGS
2
2
There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf Keywords:} multiplicative hyperring, derivation, differential hyperring.
1

21
35


L.
Kamali Ardekani
Yazd University
Yazd University
Iran
kamali_leili@yahoo.com


Bijan
Davvaz
Yazd University
Yazd University
Iran
davvaz@yazd.ac.ir
multiplicative hyperring
derivation
differential hyperring
A CHARACTERIZATION OF BAERIDEALS
2
2
An ideal I of a ring R is called right Baerideal if there exists an idempotent e 2 R such that r(I) = eR. We know that R is quasiBaer if every ideal of R is a right Baerideal, R is ngeneralized right quasiBaer if for each I E R the ideal In is right Baerideal, and R is right principaly quasiBaer if every principal right ideal of R is a right Baerideal. Therefore the concept of Baer ideal is important. In this paper we investigate some properties of Baerideals and give a characterization of Baerideals in 2by2 generalized triangular matrix rings, full and upper triangular matrix rings, semiprime ring and ring of continuous functions. Finally, we find equivalent conditions for which the 2by2 generalized triangular matrix ring is right SA.
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37
51


Ali
Taherifar
Yasouj University
Yasouj University
Iran
ataherifar54@gmail.com
QuasiBaer ring
Generalized right quasiBaer
Semicentral idempotent
Spec(R)
Extremally disconnected space
APPROXIMATE IDENTITY IN CLOSED CODIMENSION ONE IDEALS OF SEMIGROUP ALGEBRAS
2
2
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 abounded approximate identity in closed codimension one ideals of the semigroup algebra $M_a(S)$ of a locally compact topological foundationsemigroup with identity.
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53
59


bharam
Mohammadzadeh
Babol university of technology Babol Iran
Babol university of technology Babol Iran
Iran
b.mohammadzadeh@nit.ac.ir
Approximate identity
codimension one ideal
foundation semigroup
semigroup algebras
LIFTING MODULES WITH RESPECT TO A PRERADICAL
2
2
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 $N=N_1oplusN_2$ is $tau_M$lifting. We investigate when homomorphic image of a $tau_M$lifting moduleis $tau_M$lifting.
1

61
65


Tayyebeh
Amouzegar
Department of Mathematics,
Quchan Institute of Engineering
and Technology, Quchan, Iran
Department of Mathematics,
Quchan Institute
Iran
t.amoozegar@yahoo.com
preradical
hereditary
$tau_M$lifting module
BEST APPROXIMATION IN QUASI TENSOR PRODUCT SPACE AND DIRECT SUM OF LATTICE NORMED SPACES
2
2
We study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesX_{i}. We introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by X boxtimesY. We investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor 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 withdownward and upward subsets of the direct sum of lattice normedspaces X_{i} is discussed. This will be done by homomorphismfunctions. Finally, we introduce the best approximation of thesesets.
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67
81


Mahdi
Iranmanesh
Department of Mathematics,.Shahrood University of Tecnology, Shahrood, Iran. P.O.BOX 3619995161316
Department of Mathematics,.Shahrood University
Iran
m.iranmanesh@shahroodut.ac.ir


Fateme
Solimani
Department of mathematical sciences, Shahrood university of technology
Department of mathematical sciences, Shahrood
Iran
enfazh.bmaam@gmail.com
Best approximation
proximinal set
downward set
tensor product
quasi tensor product