Good rings and homogeneous polynomials

نویسندگان

چکیده

In 2011, Khurana, Lam and Wang defined the following property: (*) A commutative unital ring satisfies property “power stable range one” if for all a,b∈A with aA+bA=A there is an integer N=N(a,b)≥1 λ=λ(a,b)∈A such that bN+λa∈A×, unit group of A. 2019, Berman Erman considered rings (**) has enough homogeneous polynomials any k≥1 set S:={p1,p2,…⁡,pk}, primitive points in An n≥2, exists a polynomial P(X1,X2,…⁡,Xn)∈A[X1,X2,…⁡,Xn] deg P≥1 P(pi)∈A× 1≤i≤k. We show two properties are equivalent we shall call these good ring. When pictorsion as by Gabber, Lorenzini Liu 2015, Using Dedekind domain built Goldman 1963, converse false.

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ژورنال

عنوان ژورنال: Journal of Commutative Algebra

سال: 2022

ISSN: ['1939-0807', '1939-2346']

DOI: https://doi.org/10.1216/jca.2022.14.527