THE FRATTINI SUBSEMIGROUP OF THE MULTIPLICATIVE MONOID OF A FINITE SPECIAL PRINCIPAL IDEAL RING
David E. Dobbs, Brian C. Irick · 2012
The Frattini subsemigroup of a finite semigroup S is introduced as the intersection of the maximal subsemigroups ofS and is characterized, in caseS is finite with more than one element, as the set of all the semigroup- theoretic nongenerators of S. As an application, the Frattini subsemigroup of the multiplicative monoid of a finite special principal ideal ring (SPIR) (R;M) which is not a field is computed as the disjoint union ofM 2 and the Frattini subgroup of the group of units ofR.