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Currently displaying 1 – 20 of 40

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Congruences on strong semilattices of regular simple semigroups.

Mario Petrich — 1988

Semigroup forum

Sur la décomposition demi-réticulée maximale d'un demi-groupe

Séminaire Dubreil. Algèbre et théorie des nombres

L'enveloppe de translations d'un demi-treillis de groupes

Séminaire Dubreil. Algèbre et théorie des nombres

Two Congruence Lattices of Completely Simple Semigroups.

Mario Petrich — 1993

Monatshefte für Mathematik

The maximal semilattice decomposition of a semigroup.

Mario Petrich. — 1964

Mathematische Zeitschrift

All subvarieties of a certain variety of semigroups.

Mario Petrich — 1974

Semigroup forum

Dense extensions of completely 0-simple semigroups. II.

Mario Petrich — 1973

Journal für die reine und angewandte Mathematik

Dense extensions of completely 0-simple semigroups. I.

Mario Petrich — 1973

Journal für die reine und angewandte Mathematik

Completely semisimple semigroups whose idempotents from a tree.

Mario Petrich — 1976

Journal für die reine und angewandte Mathematik

Free inverse semigroups

Mario Petrich — 1990

Colloquium Mathematicae

Extensions normales de demi-groupes inverses

Mario Petrich — 1981

Fundamenta Mathematicae

Some relations on the lattice of varieties of completely regular semigroups

Mario Petrich — 2002

Bollettino dell'Unione Matematica Italiana

On the lattice $L (C R)$ of varieties of completely regular semigroups considered as algebras with the binary multiplication and unary inversion within maximal subgroups, we study the relations $K_{l}$ , $K$ , $K_{r}$ , $T_{l}$ , $T$ , $T_{r}$ , $C$ and $L$ . Here $K$ is the kernel relation, $T$ is the trace relation, $T_{l}$ and $T_{r}$ are the left and the right trace relations, respectively, $K_{p} = K \cap T_{p}$ for $p \in \{l, r\}$ , $C$ is the core relation and $L$ is the local relation. We give an alternative definition for each of these relations $P$ of the form $U P V \Leftrightarrow U \cap \tilde{P} = V \cap \tilde{P} (U, V \in L (C R)),$ for some subclasses $\tilde{P}$ of $C R$ ....

Certain partial orders on semigroups

Mario Petrich — 2001

Czechoslovak Mathematical Journal

Relations introduced by Conrad, Drazin, Hartwig, Mitsch and Nambooripad are discussed on general, regular, completely semisimple and completely regular semigroups. Special properties of these relations as well as possible coincidence of some of them are investigated in some detail. The properties considered are mainly those of being a partial order or compatibility with multiplication. Coincidences of some of these relations are studied mainly on regular and completely regular semigroups.

On the structure of a class of commutative semigroups

Mario Petrich — 1964

Czechoslovak Mathematical Journal

Prime ideals of the cartesian product of two semigroups

Mario Petrich — 1962

Czechoslovak Mathematical Journal

Characterizing pure, cryptic and Clifford inverse semigroups

Mario Petrich — 2014

Czechoslovak Mathematical Journal

An inverse semigroup $S$ is pure if $e = e^{2}$ , $a \in S$ , $e < a$ implies $a^{2} = a$ ; it is cryptic if Green’s relation $ℋ$ on $S$ is a congruence; it is a Clifford semigroup if it is a semillatice of groups. We characterize the pure ones by the absence of certain subsemigroups and a homomorphism from a concrete semigroup, and determine minimal nonpure varieties. Next we characterize the cryptic ones in terms of their group elements and also by a homomorphism of a semigroup constructed in the paper. We also characterize groups and...

Normal cryptogroups with an associate subgroup

Mario Petrich — 2013

Czechoslovak Mathematical Journal

Let $S$ be a semigroup. For $a, x \in S$ such that $a = a x a$ , we say that $x$ is an associate of $a$ . A subgroup $G$ of $S$ which contains exactly one associate of each element of $S$ is called an associate subgroup of $S$ . It induces a unary operation in an obvious way, and we speak of a unary semigroup satisfying three simple axioms. A normal cryptogroup $S$ is a completely regular semigroup whose $ℋ$ -relation is a congruence and $S / ℋ$ is a normal band. Using the representation of $S$ as a strong semilattice of Rees matrix semigroups,...

Bases for certain varieties of completely regular semigroups

Mario Petrich — 2021

Commentationes Mathematicae Universitatis Carolinae

Completely regular semigroups equipped with the unary operation of inversion within their maximal subgroups form a variety, denoted by $𝒞ℛ$ . The lattice of subvarieties of $𝒞ℛ$ is denoted by $ℒ (𝒞ℛ)$ . For each variety in an $⋂$ -subsemilattice $Γ$ of $ℒ (𝒞ℛ)$ , we construct at least one basis of identities, and for some important varieties, several. We single out certain remarkable types of bases of general interest. As an application for the local relation $L$ , we construct $𝐋$ -classes of all varieties in $Γ$ . Two figures illustrate...

Semigroups certain of whose subsemigroups have identities

Mario Petrich — 1966

Czechoslovak Mathematical Journal

On ideals of a semilattice

Mario Petrich — 1972

Czechoslovak Mathematical Journal

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