半群的子半群上的同余扩张(英)

Extensions of Congruences on Subsemingroups of Semigroups

英文关键词:semigroups  extension of congruence

中文摘要:

      设ρ是个群S上的一个同余．如果S／ρ是矩形带，则称ρ是矩形带同余。本文刻画了半群上的最小矩形带同余．设T是半群S的子半群，本文给出了T上每个矩形带同余能扩张成S上矩形带同余的充分必要条件。

英文摘要:

      Let ρ be a congruence on a semingroup S.ρis called a rectangular band congruence if S/ρ is a rectangular band. In this paper the least restangular band congruence on a senigroup is disccribed . Let T be a subsemigroup of a semigroup S. A necessary and sufficient condition for which every rectangular band congruence on T can be uniquely extended to a rectangular band congruence on S is given.