On an Open Problem of Hereditary Property of Green's $\mathcal{H}$-Relation on Compact Semigroups
Xiaojiang Guo, K. P. Shum · Algebra Colloquium · 2013
We give a negative answer to an open problem concerning the hereditary property of Green's [Formula: see text]-relation on a compact semigroup proposed by Carruth and Clark in 1972. In addition, we give a positive answer to this open problem by adding some suitable conditions on the compact semigroup.