2019-05-22T01:18:20Z http://jas.shahroodut.ac.ir/?_action=export&rf=summon&issue=40
2014-01-01 10.22044
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
2014-01-01 10.22044
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
2014-01-01 10.22044
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
2014-01-01 10.22044
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
2014-01-01 10.22044
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
2014-01-01 10.22044
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