On rich monoids
On right congruences associated with the input semigroup S of automata.
On right congruences of semigroups.
On right normal right inverse semigroups.
On right self-injective regular semigroups.
On rings with zero divisors. Strong -groups
On Roots of ak bl.
On Rough Subgroup of a Group
This article describes a rough subgroup with respect to a normal subgroup of a group, and some properties of the lower and the upper approximations in a group.
On Rusakov’s -ary -groups
Properties of -ary groups connected with the affine geometry are considered. Some conditions for an -ary -group to be derived from a binary group are given. Necessary and sufficient conditions for an -ary group -derived from an additive group of a field to be an -group are obtained. The existence of non-commutative -ary -groups which are not derived from any group of arity for every , is proved.
On -quasinormal and -normal subgroups of a finite group
Let be a saturated formation containing the class of supersolvable groups and let be a finite group. The following theorems are presented: (1) if and only if there is a normal subgroup such that and every maximal subgroup of all Sylow subgroups of is either -normal or -quasinormally embedded in . (2) if and only if there is a normal subgroup such that and every maximal subgroup of all Sylow subgroups of , the generalized Fitting subgroup of , is either -normal or -quasinormally...
On -skew elements in polyadic groups
On sandwich sets and congruences on regular semigroups
Let be a regular semigroup and be the set of its idempotents. We call the sets and one-sided sandwich sets and characterize them abstractly where . For such that , , we call the sandwich set of . We characterize regular semigroups in which all (or all are right zero semigroups (respectively are trivial) in several ways including weak versions of compatibility of the natural order. For every , we also define as the set of all idempotets such that, for any congruence on...
On Schur-Ostrowski type theorems for group majorizations.
On Schützenberger monoids in transformation semigroups.
On self-centralizing Sylow subgroups of order four
On self-injective semigroups satisfying the minimal conditions.
On semiabelian groups.
On semidirect and two-sided semidirect products of finite trivial monoids
On semidirect products of two finite semilattices.
On semifir monoid rings.
We give a new condition on a monoid M for the monoid ring F[M] to be a 2-fir. Furthermore, we construct a monoid M that satisfies all the currently known necessary conditions for F[M] to be a semifir and that the group of units of M is trivial, but M is not a directed union of free monoids.