Stability and amalgamation in monoids

Renshaw [(a) Proc. Lend. Math. Sec. 1986, 52 (3), 119-141; (b) Ph.D. Thesis , University of St. Andrews, 1985] proved a collection of results on flatne ss, extension, and amalgamation for semigroups, and the concept of stabilit y for S-acts was introduced in (a) and shown to be connected to amalgamatio n. We extend these results here by developing the "homoiogical" structure o f amalgamated free products of monoids and provide a new condition for amal gamation of semigroups which is shown to be weaker than those given in thes e references. We also extend one of the main results in (a).