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...

An ideal I of a ring R is called right Baer-ideal if there exists an idempotent e 2 R such that r(I) = eR. We know that R is quasi-Baer if every ideal of R is a right Baer-ideal, R is n-generalized right quasi-Baer if for each I E R the ideal In is right Baer-ideal, and R is right principaly quasi-Baer if every principal right ideal of R is a right Baer-ideal. Therefore the concept of Baer idea...