Ring of normal cones

Sunny Lukose () and A. R. Rajan ()
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Sunny Lukose: Government College for Women
A. R. Rajan: University of Kerala

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 5, 663-681

Abstract: Abstract Normal categories were introduced by Nambooripad [4], who proved that the set of normal cones in such a category forms a regular semigroup. In this paper, we specialize normal categories to what we call RR-categories, and prove that the set of normal cones in such a category forms a regular ring. As an example, we analyze the regular ring of finite-rank operators on an infinite-dimensional vector space in terms of RR-categories. This example can be realised as the characterisation of a regular ring in terms of its left ideals.

Keywords: Normal category; retraction; split inclusion; normal cone; semigroup of normal cones; regular ring; RR-category (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s13226-010-0038-5

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