Displaying similar documents to “On the construction and the realization of wild monoids”

Unified-like product of monoids and its regularity property

Esra Kırmızı Çetinalp (2024)

Czechoslovak Mathematical Journal

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We first define a new monoid construction (called unified-like product O ⋄ Ω J ) under a unified product O ⋈ J and the Schützenberger product O ⋄ J . We investigate whether this algebraic construction defined with operations of the unified and Schützenberger product specifies a monoid or not. Then, we obtain a presentation of this new product for any two monoids. Finally, we define the necessary and sufficient conditions for O ⋄ Ω J to be regular.

The minimal closed monoids for the Galois connection End - Con

Danica Jakubíková-Studenovská, Reinhard Pöschel, Sándor Radelecki (2024)

Mathematica Bohemica

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The minimal nontrivial endomorphism monoids M = End Con ( A , F ) of congruence lattices of algebras ( A , F ) defined on a finite set A are described. They correspond (via the Galois connection End - Con ) to the maximal nontrivial congruence lattices Con ( A , F ) investigated and characterized by the authors in previous papers. Analogous results are provided for endomorphism monoids of quasiorder lattices Quord ( A , F ) .

A minimal regular ring extension of C(X)

M. Henriksen, R. Raphael, R. G. Woods (2002)

Fundamenta Mathematicae

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Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,τ). We investigate when G(X) coincides with the ring C ( X , τ δ ) of continuous real-valued functions on the space ( X , τ δ ) , where τ δ is the smallest Tikhonov topology on X for which τ ⊆ τ δ and C ( X , τ δ ) is von Neumann regular. The compact and metric spaces for which G ( X ) = C ( X , τ δ ) are characterized. Necessary, and different sufficient,...

Essential P -spaces: a generalization of door spaces

Emad Abu Osba, Melvin Henriksen (2004)

Commentationes Mathematicae Universitatis Carolinae

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An element f of a commutative ring A with identity element is called a if there is a g in A such that f 2 g = f . A point p of a (Tychonoff) space X is called a P - if each f in the ring C ( X ) of continuous real-valued functions is constant on a neighborhood of p . It is well-known that the ring C ( X ) is von Neumann regular ring iff each of its elements is a von Neumann regular element; in which case X is called a P -. If all but at most one point of X is a P -point, then X is called an . In earlier work...

Skew inverse power series rings over a ring with projective socle

Kamal Paykan (2017)

Czechoslovak Mathematical Journal

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A ring R is called a right PS -ring if its socle, Soc ( R R ) , is projective. Nicholson and Watters have shown that if R is a right PS -ring, then so are the polynomial ring R [ x ] and power series ring R [ [ x ] ] . In this paper, it is proved that, under suitable conditions, if R has a (flat) projective socle, then so does the skew inverse power series ring R [ [ x - 1 ; α , δ ] ] and the skew polynomial ring R [ x ; α , δ ] , where R is an associative ring equipped with an automorphism α and an α -derivation δ . Our results extend and unify many existing...