On the construction and the realization of wild monoids

Pavel Růžička

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 $τ \subseteq τ_{δ}$ 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,...

Unit-regularity and representability for semiartinian $*$ -regular rings

Christian Herrmann (2020)

Archivum Mathematicum

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We show that any semiartinian $*$ -regular ring $R$ is unit-regular; if, in addition, $R$ is subdirectly irreducible then it admits a representation within some inner product space.

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...

The Gibbs phenomenon and Lebesgue constants for regular $A (λ)$ means

V. Swaminathan (1977)

Matematički Vesnik

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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...

About G-rings

Najib Mahdou (2017)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we are concerned with G-rings. We generalize the Kaplansky’s theorem to rings with zero-divisors. Also, we assert that if $R \subseteq T$ is a ring extension such that $m T \subseteq R$ for some regular element $m$ of $T$ , then $T$ is a G-ring if and only if so is $R$ . Also, we examine the transfer of the G-ring property to trivial ring extensions. Finally, we conclude the paper with illustrative examples discussing the utility and limits of our results.

On some noetherian rings of $C^{\infty}$ germs on a real closed field

Abdelhafed Elkhadiri (2011)

Annales Polonici Mathematici

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Let R be a real closed field, and denote by $_{R, n}$ the ring of germs, at the origin of Rⁿ, of $C^{\infty}$ functions in a neighborhood of 0 ∈ Rⁿ. For each n ∈ ℕ, we construct a quasianalytic subring $_{R, n} \subset_{R, n}$ with some natural properties. We prove that, for each n ∈ ℕ, $_{R, n}$ is a noetherian ring and if R = ℝ (the field of real numbers), then $_{ℝ, n} = ₙ$ , where ₙ is the ring of germs, at the origin of ℝⁿ, of real analytic functions. Finally, we prove the Real Nullstellensatz and solve Hilbert’s 17th Problem for the ring $_{R, n}$ . ...

Every braid admits a short sigma-definite expression

Jean Fromentin (2011)

Journal of the European Mathematical Society

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A result by Dehornoy (1992) says that every nontrivial braid admits a $σ$ -definite expression, defined as a braid word in which the generator $σ_{i}$ with maximal index $i$ appears with exponents that are all positive, or all negative. This is the ground result for ordering braids. In this paper, we enhance this result and prove that every braid admits a $σ$ -definite word expression that, in addition, is quasi-geodesic. This establishes a longstanding conjecture. Our proof uses the dual braid monoid...