The $S$-weak global dimension of commutative rings

Xiaolei Zhang

The $S$-weak global dimension of commutative rings

Commutative Algebra 2021-06-02 v1

Authors: Xiaolei Zhang

Abstract

In this paper, we introduce and study the $S$ -weak global dimension $S$ -w.gl.dim $(R)$ of a commutative ring $R$ for some multiplicative subset $S$ of $R$ . Moreover, commutative rings with $S$ -weak global dimension at most $1$ are studied. Finally, we investigated the $S$ -weak global dimension of factor rings and polynomial rings.

Keywords

commutative rings weak global dimension multiplicative subset factor rings polynomial rings

Cite

@article{arxiv.2106.00535,
  title  = {The $S$-weak global dimension of commutative rings},
  author = {Xiaolei Zhang},
  journal= {arXiv preprint arXiv:2106.00535},
  year   = {2021}
}

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