STABILITY AND AMALGAMATION IN MONOIDS

Abstract

Renshaw [(a) Proc. Lond. Math. Soc. 1986, 52 (3), 119–141; (b) Ph.D. Thesis, University of St. Andrews, 1985] proved a collection of results on flatness, extension, and amalgamation for semigroups, and the concept of stability for S-acts was introduced in (a) and shown to be connected to amalgamation. We extend these results here by developing the “homological” structure of amalgamated free products of monoids and provide a new condition for amalgamation of semigroups which is shown to be weaker than those given in these references. We also extend one of the main results in (a).

Keywords:

• Semigroup
• Monoid
• Stability
• Free-product
• Amalgamation
• Flatness
• Purity
• S-act

Acknowledgments