具有*-IFP性质的*-半环

*-semirings with *-IFP

本文研究了具有*-IFP性质的*-半环.称*-半环R具有*-IFP性质,如果对于任意的a∈R,a的右零化子是R的一个*-理想.这个定义等价于,对于任意的a,b∈R,由ab=0可推出aRb^(*)=0.我们对于这种*-半环的性质进行刻画,并给出了一些具体的例子.作为应用,我们主要研究了与这类*-半环相关的广义逆.对于加法可消、幂等元可补且具有*-IFP性质的*-半环R,如果a∈R是自反可逆的,则可以得到a是EP元、偏序等距元、正规元和强EP元的等价刻画.

We study*-semirings with*-IFP.A*-semiring R has*-IFP if for every a∈R,the right annihilator of a is a*-ideal of R,which is equivalent that ab=0 implies aRb^(*)=0 for all a,b∈R.Some characterizations and examples of this class of semirings are given.As applications,generalized inverses related to*-semirings with*-IFP are studied.For an additive cancellative and Id-complemented*-semiring R having*-IFP,if a∈R is reflexive invertible,some equivalent characterizations of a being EP elements,partial isometries,normal elements and strong EP elements are given.