Abstract

Given elements a, b, c of any associative ring R with 1, then a is called right hybrid (b, c)-invertible if there exists $y\in R$ such that $\mathit{yay}=y,yR=bR$ and rann$(y)=\text{rann}(c).$ It is shown that such y exists if and only if $c\in \mathit{cabR}$ and $\text{rann}(\mathit{cab})\subseteq \text{rann}(b),$ in which case y is unique. With an appropriate generalization of the right annhilator rann (.), this result is extended to all semigroups with 1 and to all categories. The semigroup version of right (and left) annihilator ideals is also used to define five finiteness properties for semigroups, and to establish the implications between them. Corresponding results for categories are also obtained.

摘要

给定任何具有1的关联环R的元素a，b，c，则将a称为右混合（b，c）可逆的（如果存在）$ÿ\in \mathrm{[R}$ 这样 $\mathit{耶}=ÿ，ÿ\mathrm{[R}=b\mathrm{[R}$ 跑了$（ÿ）=\text{跑了}（C）。$证明只有当且仅当这样的y存在$C\in \mathit{卡布}$ 和 $\text{跑了}（\mathit{出租车}）\subseteq \text{跑了}（b），$在这种情况下，y是唯一的。正确地概括了右角破折号rann（。），此结果将扩展到所有带有1的半群和所有类别。右（和左）an灭者理想的半组版本也用于为半组定义五个有限性属性，并确定它们之间的含义。还获得了相应的类别结果。