@article {
author = {Naghipour, A.R.},
title = {SOME RESULTS ON STRONGLY PRIME SUBMODULES},
journal = {Journal of Algebraic Systems},
volume = {1},
number = {2},
pages = {79-89},
year = {2014},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2014.228},
abstract = {Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)y P$ for $x, y M$, implies that $x P$ or $y P$. In this paper, we study more properties of strongly prime submodules. It is shown that a finitely generated $R$-module $M$ is Artinian if and only if $M$ is Noetherian and every strongly prime submodule of $M$ is maximal. We also study the strongly dimension of a module which is defined to be the length of a longest chain of strongly prime submodules.},
keywords = {Prime submodule,classical Krull dimension,strongly prime submodule},
url = {http://jas.shahroodut.ac.ir/article_228.html},
eprint = {http://jas.shahroodut.ac.ir/article_228_6566623d100f92ad63091efa325975a1.pdf}
}
@article {
author = {Nasernejad, M.},
title = {A NEW PROOF OF THE PERSISTENCE PROPERTY FOR IDEALS IN DEDEKIND RINGS AND PR¨UFER DOMAINS},
journal = {Journal of Algebraic Systems},
volume = {1},
number = {2},
pages = {91-100},
year = {2014},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2014.229},
abstract = {In this paper, by using elementary tools of commutative algebra, we prove the persistence property for two especial classes of rings. In fact, this paper has two main sections. In the first main section, we let $R$ be a Dedekind ring and $I$ be a proper ideal of $R$. We prove that if $I_1,\ldots,I_n$ are non-zero proper ideals of $R$, then ${Ass}^{\infty}(I_1^{k_1}\ldots I_n^{k_n})={Ass}^{\infty}(I_1^{k_1})\cup\cdots\cup {Ass}^{\infty}(I_n^{k_n})$ for all $k_1,\ldots,k_n \geq 1$, where for an ideal $J$ of $R$, ${Ass}^{\infty}(J)$ is the stable set of associated primes of $J$. Moreover, we prove that every non-zero ideal in a Dedekind ring is Ratliff-Rush closed, normally torsion-free and also has a strongly superficial element. Especially, we show that if $\mathcal{R}=\mathcal{R}(R, I)$ is the Rees ring of $R$ with respect to $I$, as a subring of $R[t,u]$ with $u=t^{-1}$, then $u\mathcal{R}$ has no irrelevant prime divisor. \par In the second main section, we prove that every non-zero finitely generated ideal in a Pr\"{u}fer domain has the persistence property with respect to weakly associated prime ideals.},
keywords = {Dedekind rings,Pr¨ufer domains,weakly associated prime ideals,associated prime ideals,powers of ideals},
url = {http://jas.shahroodut.ac.ir/article_229.html},
eprint = {http://jas.shahroodut.ac.ir/article_229_aedeac2f9e82c3042ad040a8f3f9241a.pdf}
}
@article {
author = {Fazaeli Moghim, H. and Rashedi, F.},
title = {ZARISKI-LIKE SPACES OF CERTAIN MODULES},
journal = {Journal of Algebraic Systems},
volume = {1},
number = {2},
pages = {101-115},
year = {2014},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2014.230},
abstract = {Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. The primary-like spectrum $Spec_L(M)$ is the collection of all primary-like submodules $Q$ such that $M/Q$ is a primeful $R$-module. Here, $M$ is defined to be RSP if $rad(Q)$ is a prime submodule for all $Q\in Spec_L(M)$. This class contains the family of multiplication modules properly. The purpose of this paper is to introduce and investigate a new Zariski space of an RSP module, called Zariski-like space. In particular, we provide conditions under which the Zariski-like space of a multiplication module has a subtractive basis.},
keywords = {RSP module,Multiplication module,Zariski-like space,Subtractive subsemi- module,Subtractive basis},
url = {http://jas.shahroodut.ac.ir/article_230.html},
eprint = {http://jas.shahroodut.ac.ir/article_230_b7b37843a5fe23f4743e67cb83ccec30.pdf}
}
@article {
author = {Hejazi, Seyed R.},
title = {CLASSIFICATION OF LIE SUBALGEBRAS UP TO AN INNER AUTOMORPHISM},
journal = {Journal of Algebraic Systems},
volume = {1},
number = {2},
pages = {117-133},
year = {2014},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2014.231},
abstract = {In this paper, a useful classification of all Lie subalgebras of a given Lie algebra up to an inner automorphism is presented. This method can be regarded as an important connection between differential geometry and algebra and has many applications in different fields of mathematics. After main results, we have applied this procedure for classifying the Lie subalgebras of some examples of Lie algebras.},
keywords = {Lie algebra,vector fields,optimal system},
url = {http://jas.shahroodut.ac.ir/article_231.html},
eprint = {http://jas.shahroodut.ac.ir/article_231_7c2bfe95b378521e2f2c00a52d821f78.pdf}
}
@article {
author = {Bakhshi, M.},
title = {Lattice of weak hyper K-ideals of a hyper K-algebra},
journal = {Journal of Algebraic Systems},
volume = {1},
number = {2},
pages = {135-147},
year = {2014},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2014.232},
abstract = {In this note, we study the lattice structure on the class of all weak hyper K-ideals of a hyper K-algebra. We first introduce the notion of (left,right) scalar in a hyper K-algebra which help us to characterize the weak hyper K-ideals generated by a subset. In the sequel, using the notion of a closure operator, we study the lattice of all weak hyper K-ideals of a hyper K-algebra, and we prove a special subclass of this class together with the suitable operations forms a Boolean lattice.},
keywords = {Hyper K-ideals,weak hyper K-ideals,Boolean lattice},
url = {http://jas.shahroodut.ac.ir/article_232.html},
eprint = {http://jas.shahroodut.ac.ir/article_232_fe64e3c27374bc5dcee6428ef6fbdbec.pdf}
}
@article {
author = {Behboodi, M. and Jahani-Nezhad, R. and Naderi, M. H.},
title = {Quasi-Primary Decomposition in Modules Over Proufer Domains},
journal = {Journal of Algebraic Systems},
volume = {1},
number = {2},
pages = {149-160},
year = {2014},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2014.233},
abstract = {In this paper we investigate decompositions of submodules in modules over a Proufer domain into intersections of quasi-primary and classical quasi-primary submodules. In particular, existence and uniqueness of quasi-primary decompositions in modules over a Proufer domain of ﬁnite character are proved. },
keywords = {Proufer domain,primary submodule,quasi-primary submodule,classical quasi-primary,Decomposition},
url = {http://jas.shahroodut.ac.ir/article_233.html},
eprint = {http://jas.shahroodut.ac.ir/article_233_7d82024d729effde8d1807391f2bc9e3.pdf}
}