The word "History" is used in the Persian Language in two meanings: 1. A collection of written scientific, theoretical and intellectual activities of the historians which is the same as "Science of History"; 2. A collection of incidents and events occurred by the human which implies history in its conventional meaning and is used without adding the word "Science". If we could determine the manner of recognition or acquiring knowledge of history in the second meaning, namely, as a collection of events, the existence of something called "Science of History" would also be proven, thus, we may say that the science of history is really a "Science". The present article by considering the ideas of scientists and historians from the earliest time up to the beginning of the twentieth century, distinguishes the two different meanings of history and follows the developments in the current outlooks about history as well as its regularity and eventuality.

In this article we give a characterization of monoids for which torsion freeness, ((principal) weak, strong) flatness, equalizer flatness or Condition (E) of finitely generated and (mono) cyclic acts and Condition (P) of finitely generated and cyclic acts implies regularity. A characterization of monoids for which all (finitely generated, (mono) cyclic acts are regular will be given too. We also show that monoids for which all regular right acts are WPF, WKF, PWKF, TKF or satisfy Conditions (P), (WP) and (PWP) are the same as those for which all regular right acts are projective or strongly flat. Monoids S with E(S)ÍC(S) or those for which every element of E(S)\{1} is right zero will be characterized, when all (finitely generated, cyclic) right S-acts satisfying Conditions (PWP), (WP), (PE) or (P) are regular. Simple monoids for which all (finitely generated, cyclic) right acts with property U (U is a property of acts over monoids implied by Condition (P)) are regular will be characterized too.

In this paper, we giving certain properties of the commuting regular semigroups, we get significant results on semigroups. Our investigation involve certain interesting class of commuting regular semigroups.