R. Nekooei
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, P.O. Box 76169133, Kerman, Iran.
[ 1 ] - On radical formula and Prufer domains
In this paper we characterize the radical of an arbitrary submodule $N$ of a finitely generated free module $F$ over a commutatitve ring $R$ with identity. Also we study submodules of $F$ which satisfy the radical formula. Finally we derive necessary and sufficient conditions for $R$ to be a Pr$ddot{mbox{u}}$fer domain, in terms of the radical of a cyclic submodule in $Rbigopl...
[ 2 ] - On SPAP-rings
In this paper we focus on a special class of commutative local rings called SPAP-rings and study the relationship between this class and other classes of rings. We characterize the structure of modules and especially, the prime submodules of free modules over an SPAP-ring and derive some basic properties. Then we answer the question of Lam and Reyes about strongly Oka ideals fam...
[ 3 ] - AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS
In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going down theorems for modules.
Co-Authors