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...

We study the time evolution of a viscous incompressible fluid with axial symmetry without swirl when initial vorticity is very concentrated in N disjoint rings. show that suitable joint limit, which both thickness rings and viscosity tend to zero, remains disjointed rings, each one them performing simple translation along axis constant speed.

• Vectorspaces over division rings • Matrices, opposite rings • Semi-simple modules and rings • Semi-simple algebras • Reduced trace and norm • Other criteria for simplicity • Involutions • Brauer group of a field • Tensor products of fields • Crossed product construction of simple algebras • Cyclic algebra construction of simple algebras • Quaternion algebras • Examples • Unramified extensions...

We study Ore extensions of non-unital associative rings. provide a characterization simple differential polynomial rings $R[x;\delta ]$, under the hypothesis that $R$ is $s$-unital and $\ker (\delta )$ contains non-zero idempotent. This

N-heterocyclic carbene (NHC) catalysis has emerged as a powerful tool for synthesis. Among its involvement in several cycloaddition-type reactions for the construction of lactams and lactones, which are abundant in biologically active molecules and broadly used as synthons for complex molecules, NHC catalysis through formal [3+3] or [4+2] strategies is noteworthy. In particular, [4+2] cycloaddi...

The purpose of this paper is to provide a criterion of an occurrence of uncountably generated uniserial modules over chain rings. As we show it suffices to investigate two extreme cases, nearly simple chain rings, i.e. chain rings containing only three twosided ideals, and chain rings with “many” two-sided ideals. We prove that there exists an ω1-generated uniserial module over every non-artini...

Nakayama (Ann. of Math. 42, 1941) showed that over an artinian serial ring every module is a direct sum of uniserial modules. Hence artinian serial rings have the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals. A ring with the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals will be called a ...