On some properties of extensions of commutative unital rings

P. V. Danchev

Plovdiv State University "Paissii Hilendarski", Plovdiv, Bulgaria

Abstract: We find necessary and sufficient conditions for the ring $R[\alpha]$ to be either a field or a domain whenever $R$ is a commutative ring with 1 and $\alpha$ is an algebraic element over $R$. This continues the studies started by Nachev (Compt. Rend. Acad. Bulg. Sci., 2004) and (Commun. Alg., 2005) as well as their generalization due to Mihovski (Compt. Rend. Acad. Bulg. Sci., 2005).

Key words: fields, domains, Noetherian rings, Arthinian rings, maximal ideals, prime ideals, units, zero divisors, regular elements, roots, polynomials.

UDC: 512.742

MSC: 13B25, 13B02, 16N40

Received: 31.10.2008

Language: English