On some properties of extensions of commutative unital rings
Автор: Danchev Peter V.
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 4 т.11, 2009 года.
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We find necessary and sufficient conditions for the ring R[α] to be either a field or a domain whenever R is a commutative ring with 1 and α 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).
Maximal ideals, prime ideals, zero divisors, regular elements, roots, fields, domains, noetherian rings, arthinian rings, units, polynomials
Короткий адрес: https://sciup.org/14318292
IDR: 14318292
Список литературы On some properties of extensions of commutative unital rings
- Lambek J. Rings and Modules.-Moscow: Mir, 1971.-In Russian.
- Lang S. Algebra.-Moscow: Mir, 1968.-In Russian.
- Mihovski S. Resultants and discriminants of polynomials over commutative rings//Compt. Rend. Acad. Bulg. Sci.-2006.-Vol. 8, № 59.-P. 799-804.
- Mollov T., Nachev N. Unit groups of commutative group rings//Compt. Rend. Acad. Bulg. Sci.-2004.-Vol. 5, №57.-P. 9-12.
- Nachev N. Nilpotent elements and idempotents in commutative rings//Compt. Rend. Acad. Bulg. Sci.-2004.-Vol. 5, № 57.-P. 5-8.
- Nachev N. Nilpotent elements and idempotents in commutative group rings//Comm. Algebra.-2005.-Vol. 10, № 33.-P. 631-3637.
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