Right $e$-core inverse and the related generalized inverses in rings

Abstract

In this paper, some characterizations and properties of right $e$-core inverses by using right invertible element and $\{1,3e\}$-inverse are investigated. Meanwhile,  some characterizations for  a new generalized right $e$-core inverse which is called right pseudo $e$-core inverse  are also studied. The relationship between right pseudo $e$-core inverses and right $e$-core inverses are presented.