半群的有限性与同余格的链条件

On Finiteness of Semigroups and Chain Conditions on The Lattices of Their Congruences

本文讨论了两类特殊半群的矩形带的半格的有限性和完全0_-单半群的有限性在它们同余格上链条件的刻划.前者得出有限弱可换半群(有限逆半群)的矩形带的半格是有限的当且仅当它的同余格满足 ACC 或 DCC.后者讨论了其夹心阵具列(行)正规性的完全0_-单半群在它不含无限子群时它的有限性与其同余格的链条件之间的关系.

In this paper,we discuss the characterization of finiteness ofSemilattices of rectangular bards of the two special kinds of semi-groups and finiteness of completely O-simple semigroups by chainconditions on the lattices of their congruences.We obtain that a semilatticeof rectangular bands of finite weakly commutative semigroups(finiteinverse semigroups)is finite iff the lattice of its congruences satisfies ACCor DCC.And we also discuss the relation between chain conditions onthe lattice of its congruences and the finiteness of a completely O-simplesemigroup whose sandwish matrix has column(row)normality when it hasn'tany infinite subsemigroups.