transversal

Zhu, Normal orthodox semigroups with inverse transversals, Chin.

Blyth and Almeida Santos generalized (left) amenable partial orders on inverse semigroup to regular semigroup with an inverse transversal in [4].

[4] Let (S, (x), [less than or equal to]) be a partially ordered regular semigroup with an inverse transversal S[degrees].

If [less than or equal to] is both a left amenable partial order and a right amenable partial order on S, then [less than or equal to] is called an amenable partial order and S is called an amenable partially ordered regular semigroup with inverse transversal S[degrees].

Suppose that S is a right normal orthodox semigroup with inverse transversal S[degrees].

A HG can have two or more minimal transversals with different cardinalities; see [T.sub.1] and [T.sub.2] in 3.1.

[T.sub.1] and [T.sub.2] are minimal transversals of different sizes.

Proposition 3.2 is applied to prove two propositions (3.3 and 3.5) about minimal transversals.

Let [T.sub.1] = {[x.sub.1],...,[x.sub.t]} and [T.sub.2] = {[y.sub.1],..,[y.sub.r]} be two given minimal transversals in H.

It is a simple observation that there can only be finitely many transversals in H.