The low dimensional homology groups of the elementary group of degree two

IF 0.5 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2026-03-04 DOI:10.1007/s40062-026-00401-3

Behrooz Mirzaii, Elvis Torres Pérez

引用次数: 0

Abstract

In this article, we study the first, second, and third homology groups of the elementary group \({\textrm{E}}_2(A)\), where A is a commutative ring. In particular, we establish a refined Bloch–Wigner type exact sequence over a semilocal ring (subject to mild restrictions on its residue fields) in which either \(-1 \in ({A^\times })^2\) or \(|{A^\times }/({A^\times })^2| \le 4\).

查看原文本刊更多论文

二阶初等群的低维同调群

在本文中，我们研究了A是交换环的初等群\({\textrm{E}}_2(A)\)的第一、第二和第三同调群。特别地，我们在一个半局部环上建立了一个改进的Bloch-Wigner型精确序列（对其残馀域有轻微的限制），其中\(-1 \in ({A^\times })^2\)或\(|{A^\times }/({A^\times })^2| \le 4\)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.