Frattini theory for classes of finite universal algebras of Mal'tsev varieties.
-covering systems of subgroups for classes of -supersoluble and -nilpotent finite groups.
-quasinormal subgroups.
Group ideals in a semigroup of measures.
On compressed ideals in topological semigroups
Correction to the paper “On compressed ideals in topological semigroups”
Generalized Archimedean ideals
Some remarks on topologically semiprime ideals
On the Frattini ideal in compact semigroups
A structure theorem for right pp-semigroups with left central idempotents
The concept of strong spined product of semigroups is introduced. We first show that a semigroup S is a rpp-semigroup with left central idempotents if and only if S is a strong semilattice of left cancellative right stripes. Then, we show that such kind of semigroups can be described by the strong spined product of a C-rpp-semigroup and a right normal band. In particular, we show that a semigroup is a rpp-semigroup with left central idempotents if and only if it is a right bin.
An equational axiomatization of Post Almost Distributive Lattices
In this paper, we prove that the class of P₂-Almost Distributive Lattices and Post Almost Distributive Lattices are equationally definable.
Completely prime ideals and idempotents in mobs
On compact -semigroups
Pseudo-symmetric ideals of semigroup and their radicals
Characterizations of dual semigroups
A note in inverse and dual semigroups
On super hamiltonian semigroups
The concept of super hamiltonian semigroup is introduced. As a result, the structure theorems obtained by A. Cherubini and A. Varisco on quasi commutative semigroups and quasi hamiltonian semigroups respectively are extended to super hamiltonian semigroups.
Green's relations and their generalizations on semigroups
Green's relations and their generalizations on semigroups are useful in studying regular semigroups and their generalizations. In this paper, we first give a brief survey of this topic. We then give some examples to illustrate some special properties of generalized Green's relations which are related to completely regular semigroups and abundant semigroups.
Clifford semifields
It is well known that a semigroup S is a Clifford semigroup if and only if S is a strong semilattice of groups. We have recently extended this important result from semigroups to semirings by showing that a semiring S is a Clifford semiring if and only if S is a strong distributive lattice of skew-rings. In this paper, we introduce the notions of Clifford semidomain and Clifford semifield. Some structure theorems for these semirings are obtained.
On the divisibility of power LCM matrices by power GCD matrices
Let be a set of distinct positive integers and an integer. Denote the power GCD (resp. power LCM) matrix on having the -th power of the greatest common divisor (resp. the -th power of the least common multiple ) as the -entry of the matrix by (resp. . We call the set an odd gcd closed (resp. odd lcm closed) set if every element in is an odd number and (resp. ) for all . In studying the divisibility of the power LCM and power GCD matrices, Hong conjectured in 2004 that...
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