Annihilators in ℕ^k-graded and ℤ^k-graded rings

2017/03/06 by Thomas Huettemann, Huettemann, Thomas
Mathematics · #16A03 (primary) #16A99 (secondary) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:16A03 #msc:16A99

paper · pdf · doi:10.48550/arxiv.1703.01796

8 pages; v2: minor changes; v3: generalised results slightly

openalex publication_date 2017/03/06 · arxiv created 2018/01/09 · arxiv updated 2018/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It has been shown by McCoy that a right ideal of a polynomial ring with several indeterminates has a non-trivial homogeneous right annihilator of degree 0 provided its right annihilator is non-trivial to begin with. In this note, it is documented that any ℕ-graded ring R has a slightly weaker property: the right annihilator of a right ideal contains a homogeneous non-zero element, if it is non-trivial to begin with. If R is a subring of a ℤ^k -graded ring S satisfying a certain non-annihilation property (which is the case if S is strongly graded, for example), then it is possible to find annihilators of degree 0.

Citations

• Remarks on Divisors of Zero

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