On a connection between local rings and their associated graded algebras

Hoffmeier, Justin; Lee, Jiyoon

doi:10.2140/involve.2018.11.355

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On a connection between local rings and their associated graded algebras

Justin Hoffmeier and Jiyoon Lee

Vol. 11 (2018), No. 2, 355–359

DOI: 10.2140/involve.2018.11.355

Abstract

We study a class of local rings and a local adaptation of the homogeneous property for graded rings. While the rings of interest satisfy the property in the local case, we show that their associated graded $k$ -algebras do not satisfy the property in the graded case.

Keywords

associated graded, graded algebra

Mathematical Subject Classification 2010

Primary: 13A02

Milestones

Received: 19 May 2017

Revised: 5 July 2017

Accepted: 17 July 2017

Published: 17 September 2017

Communicated by Vadim Ponomarenko

Authors

Justin Hoffmeier
Department of Mathematics and Statistics Northwest Missouri State University Maryville, MO United States

Jiyoon Lee
Missouri Academy of Science, Mathematics and Computing Maryville, MO United States

Vol. 11, No. 2, 2018