A Note on the Dimension Theory of ℤn-Graded Rings

Abstract In this note we want to generalize some of the results in [Citation1] from polynomial rings in several indeterminates to arbitrary ℤ n -graded commutative rings. We will prove an analogue of Jaffard's Special Chain Theorem and a similar result for the height of a prime ideal 𝔭 over its graded core 𝔭*. Key Words: Graded ringHeightKrull dimensionPrime ideal chain2000 Mathematics Subject Classification: Primary 13A02, 13C15Secondary 13B25 Notes Communicated by I. Swanson.