On distributively generated near-rings with generators forming inverse semigroups (Q1820224)

\textit{S. J. Mahmood}, \textit{J. D. P. Meldrum}, and \textit{L. O'Carroll} established the link between inverse semigroups and near-rings [J. Lond. Math. Soc., II. Ser. 23, 45-60 (1981; Zbl 0457.20056)]. The present author studies right near-rings N distributively generated by a regular semigroup D of distributive elements of N. Conditions (characterizations) for the following cases are obtained: 1) D is an inverse semigroup, and all idempotents of D are contained in the multiplicative center of N. 2) D is a group. Particular emphasis is given to the case, where the additive group of N is torsion free.