The least separative congruence on a weakly commutative semigroup
On congruence permutable -sets
An algebraic structure is said to be congruence permutable if its arbitrary congruences and satisfy the equation , where denotes the usual composition of binary relations. To an arbitrary -set satisfying , we assign a semigroup on the base set containing a zero element , and examine the connection between the congruence permutability of the -set and the semigroup .
On the probability that two elements of a finite semigroup have the same right matrix
We study the probability that two elements which are selected at random with replacement from a finite semigroup have the same right matrix.
On special Rees matrix semigroups over semigroups
We study the right regular representation of special Rees matrix semigroups over semigroups, and discuss their embedding in idempotent-free left simple semigroups.
On a probabilistic problem on finite semigroups
We deal with the following problem: how does the structure of a finite semigroup depend on the probability that two elements selected at random from , with replacement, define the same inner right translation of . We solve a subcase of this problem. As the main result of the paper, we show how to construct not necessarily finite medial semigroups in which the index of the kernel of the right regular representation equals two.
Page 1