Journal of Pure and Applied Algebra最新文献

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Derived complete complexes at weakly proregular ideals

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-02-14 DOI: 10.1016/j.jpaa.2025.107909

Amnon Yekutieli

Weak proregularity of an ideal in a commutative ring is a subtle generalization of the noetherian property of the ring. Weak proregularity is of special importance for the study of derived completion, and it occurs quite often in non-noetherian rings arising in Hochschild and prismatic cohomologies.

This paper is about several related topics: adically flat modules, recognizing derived complete complexes, the structure of the category of derived complete complexes, and a derived complete Nakayama theorem – all with respect to a weakly proregular ideal; and the preservation of weak proregularity under completion of the ring.

引用次数: 0

Codimension two torus actions on the affine space 仿射空间上的二维转矩作用

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-02-14 DOI: 10.1016/j.jpaa.2025.107911

Alvaro Liendo , Charlie Petitjean

In this paper, we classify smooth, contractible affine varieties equipped with faithful torus actions of complexity two, having a unique fixed point and a two-dimensional algebraic quotient isomorphic to a toric blow-up of a toric surface. These varieties are of particular interest as they represent the simplest candidates for potential counterexamples to the linearization conjecture in affine geometry.

引用次数: 0

Reducibility by polynomial functions

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-02-12 DOI: 10.1016/j.jpaa.2025.107907

Riccardo Camerlo , Carla Massaza

We study the preorder

\leq_{Pol}

(and the associated equivalence relation

\equiv_{Pol}

) on the family of subsets of an algebraically closed field k of characteristic 0, defined by letting

A \leq_{Pol} B

iff there exists a polynomial P such that

A = P^{- 1} (B)

. We concentrate mainly on the finite subsets of k and prove that the

\equiv_{Pol}

-equivalence classes of sets of a given finite cardinality form an affine algebraic variety; inside these varieties, we compute in particular the dimension of the set of

\equiv_{Pol}

-classes that have less representatives than the generic ones and the dimension of the set of

\equiv_{Pol}

-classes that are comparable with a given

\equiv_{Pol}

-class.

We also show that, in a specified sense, very many

\equiv_{Pol}

-classes are

\leq_{Pol}

-maximal (or

\leq_{Pol}

-maximal under the class of singletons, for

\equiv_{Pol}

-classes of finite sets).

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引用次数: 0

Relative Koszul coresolutions and relative Betti numbers

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-02-10 DOI: 10.1016/j.jpaa.2025.107905

Hideto Asashiba

Let G be a finitely generated right A-module for a finite-dimensional algebra A over a field

k

, and

I

the additive closure of G. We will define an

I

-relative Koszul coresolution

of an indecomposable direct summand V of G, and show that for a finitely generated A-module M, the

I

-relative i-th Betti number for M at V is given as the

k

-dimension of the i-th homology of the

I

-relative Koszul complex

of M at V for all

i \geq 0

. This is applied to investigate the minimal interval resolution/coresolution of a persistence module M, e.g., to check the interval decomposability of M, and to compute the interval approximation of M.

引用次数: 0

Minimal resolutions of lattice ideals

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-02-07 DOI: 10.1016/j.jpaa.2025.107901

Yupeng Li , Ezra Miller , Erika Ordog

A canonical minimal free resolution of an arbitrary co-artinian lattice ideal over the polynomial ring is constructed over any field whose characteristic is 0 or any but finitely many positive primes. The differential has a closed-form combinatorial description as a sum over lattice paths in

Z^{n}

of weights that come from sequences of faces in simplicial complexes indexed by lattice points. Over a field of any characteristic, a non-canonical but simpler resolution is constructed by selecting choices of higher-dimensional analogues of spanning trees along lattice paths. These constructions generalize sylvan resolutions for monomial ideals by lifting them equivariantly to lattice modules.

引用次数: 0

On pyramidal groups of prime power degree

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107868

Xiaofang Gao , Martino Garonzi

A Kirkman Triple System Γ is called m-pyramidal if there exists a subgroup G of the automorphism group of Γ that fixes m points and acts regularly on the other points. Such group G admits a unique conjugacy class C of involutions (elements of order 2) and

| C | = m

. We call groups with this property m-pyramidal. We prove that, if m is an odd prime power

p^{k}

, with

p \neq 7

, then every m-pyramidal group is solvable if and only if either

m = 9

or k is odd. The primitive permutation groups play an important role in the proof. We also determine the orders of the m-pyramidal groups when m is a prime number.

引用次数: 0

Categories of sets with infinite addition

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107872

Pablo Andrés-Martínez , Chris Heunen

We consider sets with infinite addition, called Σ-monoids, and contribute to their literature in three ways. First, our definition subsumes those from previous works and allows us to relate them in terms of adjuctions between their categories. In particular, we discuss Σ-monoids with additive inverses. Second, we show that every Hausdorff commutative monoid is a Σ-monoid, and that there is a free Hausdorff commutative monoid for each Σ-monoid. Third, we prove that Σ-monoids have well-defined tensor products, unlike topological abelian groups.

引用次数: 0

Steenrod closed parameter ideals in the mod-2 cohomology of A4 and SO(3)

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107899

Henrik Rüping , Marc Stephan , Ergün Yalçın

In this paper, we classify the parameter ideals in

H^{⁎} (B A_{4}; F_{2})

and in the Dickson algebra

H^{⁎} (B SO (3); F_{2})

that are closed under Steenrod operations. Consequently, we obtain restrictions on the dimensions

n, m

for which

A_{4}

(and

SO (3)

) can act freely on

S^{n} \times S^{m}

引用次数: 0

Retraction notice to “Corrigendum to ‘On the fifth Singer algebraic transfer in a generic family of internal degree characterized by μ(n)=4’ [J. Pure Appl. Algebra 228 (2024) 107658]”

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107908

Đặng Võ Phúc

引用次数: 0

Combinatorial model categories are equivalent to presentable quasicategories

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2024.107860

Dmitri Pavlov

We establish a Dwyer–Kan equivalence of relative categories of combinatorial model categories, presentable quasicategories, and other models for locally presentable

(\infty, 1)

-categories. This implies that the underlying quasicategories of these relative categories are also equivalent. This article is also available at arXiv:2110.04679v3.

引用次数: 0

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