On the G-quadratic and LG-quadratic of the Exterior Algebra and Associated Algebra

Ruaa Yousuf Jawad

doi:10.24996/ijs.2023.64.7.24

Authors

Ruaa Yousuf Jawad Technical Instructors Training Institute, Middle Technical University, Baghdad, Iraq https://orcid.org/0000-0002-7293-4684

DOI:

https://doi.org/10.24996/ijs.2023.64.7.24%20%20

Keywords:

Initial ideal, Exterior algebra, Associated algebra, G-quadratic, LG-quadratic

Abstract

Given an exterior algebra over a finite dimension vector space v, and let , where is a graded ideal in . The relation between the algebra and regarding to -quadratic and - quadratic will be investigated. We show that the algebra is - quadratic if and only if is - quadratic. Furthermore, it has been shown that the algebra is - quadratic if and only if is - quadratic.