1. SOME RESULTS ON STRONGLY PRIME SUBMODULES

A.R. Naghipour

Volume 1, Issue 2 , Winter and Spring 2014, 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 $(P + Rx : M)y P$ 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 ...  Read More

2. A NEW PROOF OF THE PERSISTENCE PROPERTY FOR IDEALS IN DEDEKIND RINGS AND PR¨UFER DOMAINS

M. Nasernejad

Volume 1, Issue 2 , Winter and Spring 2014, 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, 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 $I_1,\ldots,I_n$ ...  Read More

3. ZARISKI-LIKE SPACES OF CERTAIN MODULES

H. Fazaeli Moghim; F. Rashedi

Volume 1, Issue 2 , Winter and Spring 2014, 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 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 ...  Read More

4. CLASSIFICATION OF LIE SUBALGEBRAS UP TO AN INNER AUTOMORPHISM

Seyed R. Hejazi

Volume 1, Issue 2 , Winter and Spring 2014, Pages 117-133

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, ...  Read More

5. Lattice of weak hyper K-ideals of a hyper K-algebra

M. Bakhshi

Volume 1, Issue 2 , Winter and Spring 2014, 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 ...  Read More

6. Quasi-Primary Decomposition in Modules Over Proufer Domains

M. Behboodi; R. Jahani-Nezhad; M. H. Naderi

Volume 1, Issue 2 , Winter and Spring 2014, 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.   Read More