Classifications of quasitrivial semigroups

in Semigroup Forum (2020), 100(3), 743-764

We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In ... [more ▼]

We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups, we address and solve several related enumeration problems. [less ▲]

Quasitrivial semigroups: characterizations and enumerations

in Semigroup Forum (2019), 98(3), 472498

We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order ... [more ▼]

We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine explicitly the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer sequences. [less ▲]

A characterization of n-associative, monotone, idempotent functions on an interval that have neutral elements

in Semigroup Forum (2018)

We investigate monotone idempotent n-ary semigroups and provide a generalization of the Czogala–Drewniak Theorem, which describes the idempotent monotone associative functions having a neutral element. We ... [more ▼]

We investigate monotone idempotent n-ary semigroups and provide a generalization of the Czogala–Drewniak Theorem, which describes the idempotent monotone associative functions having a neutral element. We also present a complete characterization of idempotent monotone n-associative functions on an interval that have neutral elements. [less ▲]

Associative and preassociative functions

in Semigroup Forum (2014), 89(2), 431-442

We investigate the associativity property for functions of multiple arities and introduce and discuss the more general property of preassociativity, a generalization of associativity which does not ... [more ▼]

We investigate the associativity property for functions of multiple arities and introduce and discuss the more general property of preassociativity, a generalization of associativity which does not involve any composition of functions. [less ▲]

Generalized entropy in expanded semigroups and in algebras with neutral element

in Semigroup Forum (2014)

The complex product of (non-empty) subalgebras of a given algebra from a variety V is again a subalgebra if and only if the variety V has the so-called generalized entropic property. This paper is devoted ... [more ▼]

The complex product of (non-empty) subalgebras of a given algebra from a variety V is again a subalgebra if and only if the variety V has the so-called generalized entropic property. This paper is devoted to algebras with a neutral element or with a semigroup operation. We investigate relationships between the generalized entropic property and the commutativity of the fundamental operations of the algebra. In particular, we characterize the algebras with a neutral element that have the generalized entropic property. Furthermore, we show that, similarly as for n-monoids and n-groups, for inverse semigroups, the generalized entropic property is equivalent to commutativity. [less ▲]

A description of n-ary semigroups polynomial-derived from integral domains

in Semigroup Forum (2011), 83(2), 241-249

We provide a complete classification of the n-ary semigroup structures defined by polynomial functions over infinite commutative integral domains with identity, thus generalizing Glazek and Gleichgewicht ... [more ▼]

We provide a complete classification of the n-ary semigroup structures defined by polynomial functions over infinite commutative integral domains with identity, thus generalizing Glazek and Gleichgewicht's classification of the corresponding ternary semigroups. [less ▲]