Ring-theoretic properties of commutative algebras of invariants

Issai Kantor, Louis H. Rowen

Research output: Contribution to journalArticlepeer-review


The commutative algebra of invariants of a Lie super-algebra need not be affine, but does have a common ideal with an affine algebra, in all the known examples. This leads us to extend a class of algebras C to a class which we call "nearly C", by admitting those algebras C having a common ideal A with an algebra (containing C) in C such that C/A ∈ C. We generalize this notion slightly, study the prime ideals of such algebras, and extend some of the standard theorems about affine algebras, Noetherian rings, and Dedekind domains. Our main theorem is that nearly affine domains are catenary, and the Krull dimension equals the transcendence degree of the quotient field. Nevertheless, it is known that nearly affine domains need not be Mori.

Original languageEnglish
Pages (from-to)239-260
Number of pages22
JournalJournal of Algebra
Issue number1
StatePublished - 1 Aug 2003


  • Affine
  • Catenary
  • Complete integral closure
  • Dedekind
  • Nearly Noetherian
  • Nearly affine
  • Nearly dedekind
  • Neotherian
  • Prime spectrum


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