The Gaussian property for rings and polynomials

• Autores: Thomas G. Lucas
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 1, 2008, págs. 1-18
• Idioma: inglés
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• Resumen

  • The content of a polynomial f over a commutative ring R is the ideal c(f) of R generated by the coefficients of f. If c(fg)=c(f)c(g) for each polynomial g in R[x], then f is said to be Gaussian. The ring R is Gaussian if each polynomial in R[x] is Gaussian. It is known that f is Gaussian if c(f) is locally principal. The converse is established for polynomials over reduced rings. Also, if the square of the nilradical is zero, then R is Gaussian if and only if the square of each finitely generated ideal is locally principal