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http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17443
Title: | On minimal ring extensions |
Authors: | Kumar, Rahul |
Keywords: | Mathematics Algebra |
Issue Date: | May-2020 |
Abstract: | Let R be a commutative ring with identity. The ring R×R can be viewed as an extension of R via the diagonal map Δ:R↪R×R, given by Δ(r)=(r,r) for all r∈R. It is shown that, for any a,b∈R, the extension Δ(R)[(a,b)]⊂R×R is a minimal ring extension if and only if the ideal <a−b> is a maximal ideal of R. A complete classification of maximal subrings of R(+)R is also given. The minimal ring extension of a von Neumann regular ring R is either a von Neumann regular ring or the idealization R(+)R/m where m∈Max(R). If R⊂T is a minimal ring extension and T is an integral domain, then (R:T)=0 if and only if R is a field and T is a minimal field extension of R, or RJ is a valuation ring of altitude one and TJ is its quotient field. |
URI: | https://arxiv.org/abs/2005.07217 http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17443 |
Appears in Collections: | Department of Mathematics |
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