幂等元位于中心的半群的局部化和最小幂幺半群同余

The localization of semigroups with cetral idempotents and the smallest unipotent semigroup congruences

局部化是交换代数的重要工具[1],证明幂等元位于中心的半群在其幂等元半格上的局部化存在且唯一,并给出此类半群的最小幂幺半群同余.另外,给出了若干半群的重要同余的刻划.

The localization is an important concept and method in commutative algebra. In this paper, we prove that the localiation of a semigroup with central idempotents on the hand of its idempotents exists and is unique. As a corollary, the smallest unipotent semigroup congruence on such semigroup is given. In addition, Important congruences on some semigroups are characterized.