F-algebraic extensions of rings
type: Item
instance of: scholarly article
title: F-algebraic extensions of rings
zbMATH Open document ID: 0532.16018
DOI: 10.1007/BF01193909
author: G. Felzenszwalb
author: Antonio Giambruno
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: Let R be an algebra over a field F and A a subalgebra of R. The algebra R is F-algebraic over A if given \(r\in R\) there exists a non-constant polynomial \(p_ r(t)\in F[t]\) such that \(p_ r(r)\in A\). We prove that if R has no non-zero algebraic ideals, then (i) if A has no non-zero algebraic right ideals neither does R; (ii) if A is a domain, R is a domain; (iii) if A has no nilpotent elements, R has no nilpotent elements. We also show that if R has no non-zero algebraic right ideals neither does A and if R is prime, A is also prime. We are finally concerned with some questions about algebraic right ideals of an algebra R.
Mathematics Subject Classification ID: 16S20
Mathematics Subject Classification ID: 16Dxx
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 3843951
zbMATH Keywords: algebraic algebra
zbMATH Keywords: algebraic ideals
zbMATH Keywords: algebraic right ideals
zbMATH Keywords: nilpotent elements
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01193909
OpenAlex ID: W2069254274
description: scientific article; zbMATH DE number 3843951