Journal of Algebra最新文献_第8页

Cluster expansions: T-walks, labeled posets and matrix calculations

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-02-06 DOI: 10.1016/j.jalgebra.2025.01.024

Ezgi Kantarcı Oğuz , Emine Yıldırım

引用次数: 0

Vishik equivalence and similarity of quadratic forms over fields of characteristic 2

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-02-05 DOI: 10.1016/j.jalgebra.2025.02.003

Detlev W. Hoffmann , Kristýna Zemková

{"title":"Vishik equivalence and similarity of quadratic forms over fields of characteristic 2","authors":"Detlev W. Hoffmann , Kristýna Zemková","doi":"10.1016/j.jalgebra.2025.02.003","DOIUrl":"10.1016/j.jalgebra.2025.02.003","url":null,"abstract":"<div><div>An important aspect in the algebraic theory of quadratic forms is the study of equivalence relations based on algebraic-geometric properties of the associated quadrics. A well-known criterion originally proved by Vishik in characteristic zero states that two nonsingular quadratic forms of the same dimension have identical Witt indices over all field extensions if and only if their motives are isomorphic in the category of (integral or mod 2) Chow motives. In characteristic 2, it is meaningful to include singular forms. We therefore define two quadratic forms (including singular ones) of the same dimension to be Vishik-equivalent if they share the same isotropy behavior (in a suitably defined way) over all field extensions. Similar quadratic forms are always Vishik-equivalent, but the converse need not hold. We determine various classes of quadratic forms in characteristic 2 where Vishik equivalence implies similarity and give nonsingular counterexamples in all dimensions <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>≥</mo><mn>8</mn></math></span>, and also singular counterexamples in dimension 8. To construct the counterexamples, we use a generalized notion of so-called half-neighbors in characteristic 2.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"669 ","pages":"Pages 118-142"},"PeriodicalIF":0.8,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Pfaffian formulation of Schur's Q-functions

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-02-05 DOI: 10.1016/j.jalgebra.2025.02.002

John Graf, Naihuan Jing

引用次数: 0

On limit models and parametrized Noetherian rings

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-02-05 DOI: 10.1016/j.jalgebra.2025.02.006

Marcos Mazari-Armida

{"title":"On limit models and parametrized Noetherian rings","authors":"Marcos Mazari-Armida","doi":"10.1016/j.jalgebra.2025.02.006","DOIUrl":"10.1016/j.jalgebra.2025.02.006","url":null,"abstract":"<div><div>We study limit models in the abstract elementary class of modules with embeddings as algebraic objects. We characterize parametrized noetherian rings using the degree of injectivity of certain limit models.</div><div>We show that the number of limit models and how close a ring is from being noetherian are inversely proportional.</div><div><section><p><strong>Theorem 0.1</strong></p><div><em>Let</em> <span><math><mi>n</mi><mo>≥</mo><mn>0</mn></math></span> <em>The following are equivalent.</em><ul><li><span>(1)</span><span><div><em>R is left</em> <span><math><mo>(</mo><mo><</mo><msub><mrow><mi>ℵ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span><em>-noetherian but not left</em> <span><math><mo>(</mo><mo><</mo><msub><mrow><mi>ℵ</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>)</mo></math></span><em>-noetherian.</em></div></span></li><li><span>(2)</span><span><div><em>The abstract elementary class of modules with embeddings has exactly</em> <span><math><mi>n</mi><mo>+</mo><mn>1</mn></math></span> <em>non-isomorphic λ-limit models for every</em> <span><math><mi>λ</mi><mo>≥</mo><msup><mrow><mo>(</mo><mi>card</mi><mo>(</mo><mi>R</mi><mo>)</mo><mo>+</mo><msub><mrow><mi>ℵ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup></math></span> <em>such that the class is stable in λ.</em></div></span></li></ul></div></section></div><div>We further show that there are rings such that the abstract elementary class of modules with embeddings has exactly <em>κ</em> non-isomorphic <em>λ</em>-limit models for every infinite cardinal <em>κ</em>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"669 ","pages":"Pages 58-74"},"PeriodicalIF":0.8,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A classical approach to relative quadratic extensions

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-02-05 DOI: 10.1016/j.jalgebra.2025.02.001

Hatice Boylan , Nils-Peter Skoruppa

引用次数: 0

Analogies of monic inversion principles in Laurent polynomial rings

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-02-05 DOI: 10.1016/j.jalgebra.2025.02.004

Sourjya Banerjee , Mrinal Kanti Das

引用次数: 0

Low degree motivic Donaldson-Thomas invariants of the three-dimensional projective space