@article {
author = {Aghapournahr, M. and Ahmadi-amoli, Kh. and Sadeghi, M.},
title = {THE CONCEPT OF (I; J)-COHEN MACAULAY MODULES},
journal = {Journal of Algebraic Systems},
volume = {3},
number = {1},
pages = {1-10},
year = {2015},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2015.482},
abstract = {We introduce a generalization of the notion of depth of an ideal on a module by applying the concept of local cohomology modules with respect to a pair of ideals. We also introduce the concept of $(I,J)$-Cohen--Macaulay modules as a generalization of concept of Cohen--Macaulay modules. These kind of modules are different from Cohen--Macaulay modules, as an example shows. Also an artinian result for such modules is given.},
keywords = {local cohomology modules defined by a pair of ideals,system of ideals,depth of a pair of ideals,$(I,J)$-Cohen--Macaulay modules},
url = {http://jas.shahroodut.ac.ir/article_482.html},
eprint = {http://jas.shahroodut.ac.ir/article_482_3406cd1fa845d38b77f2556344be6005.pdf}
}
@article {
author = {Karimzadeh, S. and Nekooei, R.},
title = {AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS},
journal = {Journal of Algebraic Systems},
volume = {3},
number = {1},
pages = {11-22},
year = {2015},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2015.483},
abstract = {In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going down theorems for modules.},
keywords = {Prime submodule,Integral element,Integrally closed},
url = {http://jas.shahroodut.ac.ir/article_483.html},
eprint = {http://jas.shahroodut.ac.ir/article_483_975f783e6699718e23896ed95ef10f18.pdf}
}
@article {
author = {Naghipour, A.R.},
title = {GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES},
journal = {Journal of Algebraic Systems},
volume = {3},
number = {1},
pages = {23-30},
year = {2015},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2015.484},
abstract = {The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.},
keywords = {Generalized Principal Ideal Theorem,Prime submodule,Completely prime submodule},
url = {http://jas.shahroodut.ac.ir/article_484.html},
eprint = {http://jas.shahroodut.ac.ir/article_484_b8aa3a43cefa546233e3447390d3917d.pdf}
}
@article {
author = {Afshin, H. R. and Bagheri, S. and Mehrjoofard, M. A.},
title = {GENERALIZED JOINT HIGHER-RANK NUMERICAL RANGE},
journal = {Journal of Algebraic Systems},
volume = {3},
number = {1},
pages = {31-38},
year = {2015},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2015.486},
abstract = {The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generalized numerical ranges and quantum error correction, J. Operator Theory, 66: 2, 335-351.] are extended.},
keywords = {generalized projector,joint higher rank numerical range,joint matrix numerical range,joint matrix higher rank numerical range,generalized joint higher rank
numerical range},
url = {http://jas.shahroodut.ac.ir/article_486.html},
eprint = {http://jas.shahroodut.ac.ir/article_486_30a2c8fdb2eec77f2ced44e835d901de.pdf}
}
@article {
author = {Baziar, M.},
title = {ANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS},
journal = {Journal of Algebraic Systems},
volume = {3},
number = {1},
pages = {39-47},
year = {2015},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2015.487},
abstract = {In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. Weobserve that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ isconnected and diam$Bbb{AG}_*(_RM)leq 3$. Moreover, if $Bbb{AG}_*(_RM)$ contains a cycle, then $mbox{gr}Bbb{AG}_*(_RM)leq 4$. Also for an $R$-module $M$ with$Bbb{A}_*(M)neq S(M)setminus {0}$, $Bbb{A}_*(M)=emptyset$if and only if $M$ is a uniform module and ann$(M)$ is a primeideal of $R$.},
keywords = {zero-divisor graph,Annihilating submodule graph,Weakly annihilating submodule},
url = {http://jas.shahroodut.ac.ir/article_487.html},
eprint = {http://jas.shahroodut.ac.ir/article_487_8c19ee23c3f1660ea1bf09bce9b1e051.pdf}
}
@article {
author = {Bakhshi, M.},
title = {HvMV-ALGEBRAS II},
journal = {Journal of Algebraic Systems},
volume = {3},
number = {1},
pages = {49-64},
year = {2015},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2015.488},
abstract = {In this paper, we continue our study on HvMV-algebras. The quotient structure of an HvMV-algebra by a suitable types of congruences is studied and some properties and related results are given. Some homomorphism theorems are given, as well. Also, the fundamental HvMV-algebra and the direct product of a family of HvMV-algebras are investigated and some related results are obtained.},
keywords = {MV-algebra,HvMV-algebra,HvMV-ideal,fundamental MV-algebra},
url = {http://jas.shahroodut.ac.ir/article_488.html},
eprint = {http://jas.shahroodut.ac.ir/article_488_e0ce643e38d53b19a931c7ee7e0298a6.pdf}
}
@article {
author = {Estaji, A. A. and Haghdadi, T. and Farokhi Ostad, J.},
title = {FUZZY NEXUS OVER AN ORDINAL},
journal = {Journal of Algebraic Systems},
volume = {3},
number = {1},
pages = {65-82},
year = {2015},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2015.489},
abstract = {In this paper, we define fuzzy subnexuses over a nexus $N$. Define and study the notions of the prime fuzzy subnexuses and the fractionsinduced by them. Finally, we show that if S is a meetclosed subset of the set Fsub(N), of fuzzy subnexuses of a nexus N, andh= ⋀S ϵ S, then the fractions S^-1 N and h^-1 N are isomorphic as meet-semilattices.},
keywords = {Nexus,ordinal,Prime fuzzy subnexus,Fraction
of a nexus},
url = {http://jas.shahroodut.ac.ir/article_489.html},
eprint = {http://jas.shahroodut.ac.ir/article_489_a9a4ba1f624488e61c5e37175e928284.pdf}
}
@article {
author = {Jalali, M. and Ashrafi, A. R.},
title = {COMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS},
journal = {Journal of Algebraic Systems},
volume = {3},
number = {1},
pages = {88-95},
year = {2015},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2015.490},
abstract = {Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of order $4p$ or $p^3$, where $p$ and $q$ are primes.},
keywords = {Conjugacy class,normal subset,$p-$group},
url = {http://jas.shahroodut.ac.ir/article_490.html},
eprint = {http://jas.shahroodut.ac.ir/article_490_ad72cc6d7ccfdda1a417ad5e72b51945.pdf}
}