ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS

Year 2020, Volume: 28 Issue: 28 , 175 - 186 , 14.07.2020

Pierre Landrock

https://doi.org/10.24330/ieja.768246

Cited By: 1

https://izlik.org/JA83RJ85XB

Abstract

This article is motivated by some results from Chlebowitz and Külshammer on how the structure of a symmetric local algebra is influenced by its center. They have shown that a symmetric local algebra is almost always commutative if its center is at most 5-dimensional. In this article we are interested in how the ideal property of the radical of the center of a symmetric local algebra is influenced by the dimension of the algebra itself. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

Keywords

Symmetric algebra , local algebra , radical of the center

References

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