Uniquely representable semigroups. II

Product semigroups

“…In Borrego, Cohen and DeVun (1971b) it was shown that if S is the unique product of two [/-semigroups, then S is right reversible or left reversible. The following example is due to D. Brown and J. Lawson.…”

“…PROOF. It was shown in Borrego, Cohen and DeVun (1971b) that for one [/-semigroup W to be normal in the product of two [/-semigroups WV we need only show that there exist c £ V -( 0 , l ) , w, w'E. W-{0,1} such that vw = w'v.…”

“…and L where and where R and L have the relative topology of the plane and usual matrix multiplication. Now S is the unique product of four [/-semigroups but is neither right nor left reversible, since it is the product of a semigroup R which is not left reversible by a semigroup L which is not right reversible see Borrego, Cohen and DeVun (1971b). THEOREM 1.7.…”

“…In Borrego, Cohen and DeVun (1971b) the result was shown for k -2. Assume the result holds for (n -1) products.…”

Linear representations of certain compact semigroups

“…In connection with the cancellation hypothesis of Theorem 4.1, we note that in [1] it has been shown that if M(S) is a 1-cell, and S satisfies all other hypotheses of Theorem 4.1, then S\M(S) does have cancellation. Further, no higher dimensional examples of this type are known in which S\M(S) fails to have cancellation.…”