@Article{Naghipour2014,
author="Naghipour, Alireza",
title="SOME RESULTS ON STRONGLY PRIME SUBMODULES",
journal="Journal of Algebraic Systems",
year="2014",
volume="1",
number="2",
pages="79-89",
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 $(P + Rx : M)ysubseteq P$ for $x, yin M$, implies that $xin P$ or $yin P$. 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.",
issn="2345-5128",
doi="10.22044/jas.2014.228",
url="http://jas.shahroodut.ac.ir/article_228.html"
}
@Article{Nasernejad2014,
author="Nasernejad, Mehrdad",
title="A NEW PROOF OF THE PERSISTENCE PROPERTY FOR
IDEALS IN DEDEKIND RINGS AND PR¨UFER DOMAINS",
journal="Journal of Algebraic Systems",
year="2014",
volume="1",
number="2",
pages="91-100",
abstract="In this paper, by using elementary tools of commutative algebra,we prove the persistence property for two especial classes of rings. In fact, thispaper has two main sections. In the first main section, we let R be a Dedekindring and I be a proper ideal of R. We prove that if I1, . . . , In are non-zeroproper ideals of R, then Ass1(Ik11 . . . Iknn ) = Ass1(Ik11 ) [ · · · [ Ass1(Iknn )for all k1, . . . , kn 1, where for an ideal J of R, Ass1(J) is the stable setof associated primes of J. Moreover, we prove that every non-zero ideal ina Dedekind ring is Ratliff-Rush closed, normally torsion-free and also has astrongly superficial element. Especially, we show that if R = R(R, I) is theRees ring of R with respect to I, as a subring of R[t, u] with u = t−1, then uRhas no irrelevant prime divisor.In the second main section, we prove that every non-zero finitely generatedideal in a Pr¨ufer domain has the persistence property with respect to weaklyassociated prime ideals. Finally, we extend the notion of persistence propertyof ideals to the persistence property for rings.",
issn="2345-5128",
doi="10.22044/jas.2014.229",
url="http://jas.shahroodut.ac.ir/article_229.html"
}
@Article{FazaeliMoghim2014,
author="Fazaeli Moghim, Hosein
and Rashedi, Fatemeh",
title="ZARISKI-LIKE SPACES OF CERTAIN MODULES",
journal="Journal of Algebraic Systems",
year="2014",
volume="1",
number="2",
pages="101-115",
abstract="Let $R$ be a commutative ring with identity and $M$ be a unitary$R$-module. The primary-like spectrum $Spec_L(M)$ is thecollection of all primary-like submodules $Q$ such that $M/Q$ is aprimeful $R$-module. Here, $M$ is defined to be RSP if $rad(Q)$ isa prime submodule for all $Qin Spec_L(M)$. This class containsthe family of multiplication modules properly. The purpose of thispaper is to introduce and investigate a new Zariski space of anRSP module, called Zariski-like space. In particular, we provideconditions under which the Zariski-like space of a multiplicationmodule has a subtractive basis.",
issn="2345-5128",
doi="10.22044/jas.2014.230",
url="http://jas.shahroodut.ac.ir/article_230.html"
}
@Article{Hejazi2014,
author="Hejazi, Seyed Reza",
title="Classification of Lie Subalgebras up to an Inner Automorphism",
journal="Journal of Algebraic Systems",
year="2014",
volume="1",
number="2",
pages="117-133",
abstract="In this paper, a useful classification of all Lie subalgebras of a given Lie algebraup to an inner automorphism is presented. This method can be regarded as animportant 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.",
issn="2345-5128",
doi="10.22044/jas.2014.231",
url="http://jas.shahroodut.ac.ir/article_231.html"
}
@Article{Bakhshi2014,
author="Bakhshi, Mahmood",
title="Lattice of weak hyper K-ideals of a hyper K-algebra",
journal="Journal of Algebraic Systems",
year="2014",
volume="1",
number="2",
pages="135-147",
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 ahyper K-algebra, and we prove a special subclass of this class togetherwith the suitable operations forms a Boolean lattice.",
issn="2345-5128",
doi="10.22044/jas.2014.232",
url="http://jas.shahroodut.ac.ir/article_232.html"
}
@Article{Behboodi2014,
author="Behboodi, Mahmood
and Jahani-Nezhad, Reza
and Naderi, Mohammad Hasan",
title="Quasi-Primary Decomposition in Modules Over Proufer Domains",
journal="Journal of Algebraic Systems",
year="2014",
volume="1",
number="2",
pages="149-160",
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. Proufer domain; primary submodule; quasi-primary submodule; classical quasi-primary; decomposition.",
issn="2345-5128",
doi="10.22044/jas.2014.233",
url="http://jas.shahroodut.ac.ir/article_233.html"
}