ON CHARACTERIZATION OF MONOIDS BY PROPERTIES OF GENERATORS II

Abstract

Kilp and Knauer in (Communications In Algebra, 20(7), 1841-1856, 1992) gave a characterizations of monoids when all generators in the category of right S-acts(S is a monoid) satisfy properties such as freeness, projectivity, strong flatness, Condition (P), principal weak flatness, principal weak injectivity, weak injectivity, injectivity, divisibility, strong faithfulness and torsion freeness.  Sedaghatjoo in (Semigroup Forum, 87: 653-662, 2013) gave a characterization of monoids when all generators in the category of right S-acts satisfy properties such as weak flatness, Condition (E) and regularity.  Continuing this study the authors (On characterization of monoids by properties of generators, submitted) investigated the corresponding problem for (finitely generated, cyclic, monocyclic) right acts.  To our knowledge the problem has not been yet studied for properties such as GP-flatness, strongly (P)-cyclic, (P)-regularity and Conditions (EP), (E′P), (E′), (P_E), (PW P), (PW P_E), W P F, W K F, PW K F, T K F, (W P) etc.  In this article we answer the question corresponding to these properties.