2019-05-22T01:18:20Z
http://jas.shahroodut.ac.ir/?_action=export&rf=summon&issue=40
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2014
1
2
SOME RESULTS ON STRONGLY PRIME SUBMODULES
A.R.
Naghipour
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 <br />which is defined to be the length of a longest chain of strongly prime submodules.
Prime submodule
classical Krull dimension
strongly prime submodule
2014
01
01
79
89
http://jas.shahroodut.ac.ir/article_228_6566623d100f92ad63091efa325975a1.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2014
1
2
A NEW PROOF OF THE PERSISTENCE PROPERTY FOR IDEALS IN DEDEKIND RINGS AND PR¨UFER DOMAINS
M.
Nasernejad
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 ${Ass}^{infty}(I_1^{k_1}ldots I_n^{k_n})={Ass}^{infty}(I_1^{k_1})cupcdotscup {Ass}^{infty}(I_n^{k_n})$ 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 $umathcal{R}$ 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.
Dedekind rings
Pr¨ufer domains
weakly associated prime ideals
associated prime ideals
powers of ideals
2014
01
01
91
100
http://jas.shahroodut.ac.ir/article_229_aedeac2f9e82c3042ad040a8f3f9241a.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2014
1
2
ZARISKI-LIKE SPACES OF CERTAIN MODULES
H.
Fazaeli Moghim
F.
Rashedi
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 $Qin Spec_L(M)$. 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.
RSP module
Multiplication module
Zariski-like space
Subtractive subsemi- module
Subtractive basis
2014
01
01
101
115
http://jas.shahroodut.ac.ir/article_230_b7b37843a5fe23f4743e67cb83ccec30.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2014
1
2
CLASSIFICATION OF LIE SUBALGEBRAS UP TO AN INNER AUTOMORPHISM
Seyed R.
Hejazi
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.
Lie algebra
vector fields
optimal system
2014
01
01
117
133
http://jas.shahroodut.ac.ir/article_231_7c2bfe95b378521e2f2c00a52d821f78.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2014
1
2
Lattice of weak hyper K-ideals of a hyper K-algebra
M.
Bakhshi
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.
Hyper K-ideals
weak hyper K-ideals
Boolean lattice
2014
01
01
135
147
http://jas.shahroodut.ac.ir/article_232_fe64e3c27374bc5dcee6428ef6fbdbec.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2014
1
2
Quasi-Primary Decomposition in Modules Over Proufer Domains
M.
Behboodi
R.
Jahani-Nezhad
M. H.
Naderi
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
2014
01
01
149
160
http://jas.shahroodut.ac.ir/article_233_7d82024d729effde8d1807391f2bc9e3.pdf