Birings and plethories of integer-valued polynomials

Jesse Elliott

Displaying similar documents to “Birings and plethories of integer-valued polynomials”

Generalized E-algebras via λ-calculus I

Rüdiger Göbel, Saharon Shelah (2006)

Fundamenta Mathematicae

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An R-algebra A is called an E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra $E n d_{R} A$ of the R-module $_{R} A$ , taking any a ∈ A to the right multiplication $a_{r} \in E n d_{R} A$ by a, is an isomorphism of algebras. In this case $_{R} A$ is called an E(R)-module. There is a proper class of examples constructed in [4]. E(R)-algebras arise naturally in various topics of algebra. So it is not surprising that they were investigated thoroughly in the last decades; see [3, 5, 7, 8, 10, 13, 14, 15, 18,...

Left EM rings

Jongwook Baeck (2024)

Czechoslovak Mathematical Journal

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Let $R [x]$ be the polynomial ring over a ring $R$ with unity. A polynomial $f (x) \in R [x]$ is referred to as a left annihilating content polynomial (left ACP) if there exist an element $r \in R$ and a polynomial $g (x) \in R [x]$ such that $f (x) = r g (x)$ and $g (x)$ is not a right zero-divisor polynomial in $R [x]$ . A ring $R$ is referred to as left EM if each polynomial $f (x) \in R [x]$ is a left ACP. We observe the structure of left EM rings with various properties, and study the relationships between the one-sided EM condition and other standard ring theoretic conditions....

The categories of presheaves containing any category of algebras

V. Trnková, J. Reiterman

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ContentsIntroduction.................................................................................................................................................. 5I. Preliminaries........................................................................................................................................... 6II. Main theorem.......................................................................................................................................... 8III. The...

Derived endo-discrete artin algebras

Raymundo Bautista (2006)

Colloquium Mathematicae

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Let Λ be an artin algebra. We prove that for each sequence ${(h_{i})}_{i \in ℤ}$ of non-negative integers there are only a finite number of isomorphism classes of indecomposables $X \in^{b} (Λ)$ , the bounded derived category of Λ, with $l e n g t h_{E (X)} H^{i} (X) = h_{i}$ for all i ∈ ℤ and E(X) the endomorphism ring of X in $^{b} (Λ)$ if and only if $^{b} (M o d Λ)$ , the bounded derived category of the category $M o d Λ$ of all left Λ-modules, has no generic objects in the sense of [4].

$n$ -angulated quotient categories induced by mutation pairs

Zengqiang Lin (2015)

Czechoslovak Mathematical Journal

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Geiss, Keller and Oppermann (2013) introduced the notion of $n$ -angulated category, which is a “higher dimensional” analogue of triangulated category, and showed that certain $(n - 2)$ -cluster tilting subcategories of triangulated categories give rise to $n$ -angulated categories. We define mutation pairs in $n$ -angulated categories and prove that given such a mutation pair, the corresponding quotient category carries a natural $n$ -angulated structure. This result generalizes a theorem of Iyama-Yoshino...

Schur-Finite Motives and Trace Identities

Alessio Del Padrone, Carlo Mazza (2009)

Bollettino dell'Unione Matematica Italiana

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We provide a sufficient condition that ensures the nilpotency of endomorphisms universally of trace zero of Schur-finite objects in a category of homological type, i.e., a $\mathbb{Q}$ -linear $\otimes$ -category with a tensor functor to super vector spaces. We present some applications in the category of motives, where our result generalizes previous results about finite-dimensional objects, in particular by Kimura. We also present some facts which suggest that this might be the best generalization possible...

$A F$ -algebras and topology of mapping tori

Igor Nikolaev (2015)

Czechoslovak Mathematical Journal

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The paper studies applications of $C^{*}$ -algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of $A F$ -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding $A F$ -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension $2$ , $3$ and $4$ . In conclusion, we consider two numerical examples illustrating our main results.

A Generalization of Baer's Lemma

Molly Dunkum (2009)

Czechoslovak Mathematical Journal

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There is a classical result known as Baer’s Lemma that states that an $R$ -module $E$ is injective if it is injective for $R$ . This means that if a map from a submodule of $R$ , that is, from a left ideal $L$ of $R$ to $E$ can always be extended to $R$ , then a map to $E$ from a submodule $A$ of any $R$ -module $B$ can be extended to $B$ ; in other words, $E$ is injective. In this paper, we generalize this result to the category $q_{ω}$ consisting of the representations of an infinite line quiver. This generalization of Baer’s...

One-sided $n$ -suspended categories

Jing He, Yonggang Hu, Panyue Zhou (2024)

Czechoslovak Mathematical Journal

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For an integer $n \geq 3$ , we introduce a simultaneous generalization of $(n - 2)$ -exact categories and $n$ -angulated categories, referred to as one-sided $n$ -suspended categories. Notably, one-sided $n$ -angulated categories are specific instances of this structure. We establish a framework for transitioning from these generalized categories to their $n$ -angulated counterparts. Additionally, we present a method for constructing $n$ -angulated quotient categories from Frobenius $n$ -prile categories. Our results unify...

Unimodular rows over Laurent polynomial rings

Abdessalem Mnif, Morou Amidou (2022)

Czechoslovak Mathematical Journal

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We prove that for any ring $𝐑$ of Krull dimension not greater than 1 and $n \geq 3$ , the group $E_{n} (𝐑 [X, X^{- 1}])$ acts transitively on ${Um}_{n} (𝐑 [X, X^{- 1}])$ . In particular, we obtain that for any ring $𝐑$ with Krull dimension not greater than 1, all finitely generated stably free modules over $𝐑 [X, X^{- 1}]$ are free. All the obtained results are proved constructively.