We introduce in this paper the concept of left WMC2 rings and concern ourselves with rings containing an injective maximal left ideal. Some known results for left idempotent reflexive rings and left HI rings can be extended to left WMC2 rings. As applications, we are able to give some new characterizations of regular left self-injective rings with nonzero socle and extend some known results on ...

A set of orthogonal states in multipartite systems is called to be locally stable if preserve the orthogonality states, only trivial local measurement can performed for each partite. Locally sets are always indistinguishable yielding a form nonlocality which different from Bell-type nonlocality. In this work, we study product with small size. First, give lower bound on size states. It well know...