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

Given an exterior algebra E over a finite dimension vector space v, and let R = E/I, where I is a graded ideal in E. The relation between the algebra R and Rmon regarding to G-quadratic and LG-quadratic will be investigated. We show that the algebra R is G-quadratic if and only if Rmon is G-quadratic. Furthermore, it has been shown that the algebra R is LG-quadratic if and only if Rmon is LG-quadratic. [ABSTRACT FROM AUTHOR]