A problem on bands

作者:Wang Xiangying; Liu Guoxin*
来源:Semigroup Forum, 2010, 81(3): 548-550.
DOI:10.1007/s00233-010-9233-2

摘要

In this paper, we consider an open problem proposed by Petrich and Reilly: What are necessary and sufficient conditions on a completely regular semigroup S in order that the trace relation T on the lattice of congruences on S is equal to the identity relation? By constructing some special congruences on S, we prove that T=epsilon if and only if S is a band.

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