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On homological classification of pomonoids by regular weak injectivity properties of S-posets

Xia Zhang, Valdis Laan (2007)

Open Mathematics

If S is a partially ordered monoid then a right S-poset is a poset A on which S acts from the right in such a way that the action is compatible both with the order of S and A. By regular weak injectivity properties we mean injectivity properties with respect to all regular monomorphisms (not all monomorphisms) from different types of right ideals of S to S. We give an alternative description of such properties which uses systems of equations. Using these properties we prove several so-called homological...

On special Rees matrix semigroups over semigroups

Attila Nagy, Csaba Tóth (2023)

Commentationes Mathematicae Universitatis Carolinae

We study the right regular representation of special Rees matrix semigroups over semigroups, and discuss their embedding in idempotent-free left simple semigroups.

On strongly ( P ) -cyclic acts

Akbar Golchin, Parisa Rezaei, Hossein Mohammadzadeh (2009)

Czechoslovak Mathematical Journal

By a regular act we mean an act such that all its cyclic subacts are projective. In this paper we introduce strong ( P ) -cyclic property of acts over monoids which is an extension of regularity and give a classification of monoids by this property of their right (Rees factor) acts.

Presentations for subsemigroups of P D n

Abdullahi Umar (2019)

Czechoslovak Mathematical Journal

Let [ n ] = { 1 , ... , n } be an n -chain. We give presentations for the following transformation semigroups: the semigroup of full order-decreasing mappings of [ n ] , the semigroup of partial one-to-one order-decreasing mappings of [ n ] , the semigroup of full order-preserving and order-decreasing mappings of [ n ] , the semigroup of partial one-to-one order-preserving and order-decreasing mappings of [ n ] , and the semigroup of partial order-preserving and order-decreasing mappings of [ n ] .

Principal ideals of finitely generated commutative monoids

José Carlos Rosales, Juan Ignacio García-García (2002)

Czechoslovak Mathematical Journal

We study the semigroups isomorphic to principal ideals of finitely generated commutative monoids. We define the concept of finite presentation for this kind of semigroups. Furthermore, we show how to obtain information on these semigroups from their presentations.

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