On SPAP-rings

Document Type : Research Paper


Department of‎ ‎Mathematics‎, ‎Shahid Bahonar University‎ ‎of Kerman‎, ‎P.O‎. ‎Box 76169133‎, ‎Kerman‎, ‎Iran


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 family‎. ‎Finally‎, ‎we characterize the structure of SPAP-ring in special‎ ‎cases‎.


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