Let R be an integral domain, Star(R) the set of all star operations on and StarFC(R) finite type R. Then is said to regular if |Star(T)|≤|Star(R)| for every overring T In this paper we introduce notion finitely domain as such that |StarFC(T)|≤|StarFC(R)| each First, show notions domains are completely different do not imply other. Next, extend/generalize well-known results regularity in Noether...

The main result of this paper gives a presentation for an arbitrary subgroup of a monoid defined by a presentation. It is a modification of the well known Reidemeister–Schreier theorem for groups. Some consequences of this result are explored. It is proved that a regular monoid with finitely many left and right ideals is finitely presented if and only if all its maximal subgroups are finitely p...

Let P be the variety of semigroups defined by the identity xyzx ≈ x. By a result of György Pollák, every subvariety of P is finitely based. The present article is concerned with subvarieties of P and the lattice they constitute, where the main result is a characterization of finitely generated subvarieties of P. It is shown that a subvariety of P is finitely generated if and only if it contains...