ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS

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International Electronic Journal of Algebra
Volume:28 Issue:28
ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS

ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS

Pages : 175-186

View : 39 | Download : 10

Publication Date : 2020-07-14

Article Type : Research Paper

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

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