Annihilator Primes and Foundation Primes

Širola, Boris

doi:10.1081/agb-200066186

Cited by 1 publication

(1 citation statement)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now analogously as in the commutative theory we have V(M) = cl(Ass M), the closure of the (finite) set of associated primes of M; see [31,Corollary 2.5], and also [32]. Obviously, the last equality is equivalent to the inclusion Min(ann(M)) ⊆ Ass M. Furthermore, we have Supp(M) ⊆ V(M).…”

Section: Introductionmentioning

confidence: 84%

On noncommutative Noetherian schemes

Širola

2004

Journal of Algebra

Self Cite

View full text Add to dashboard Cite

The main aim of this paper is to better understand the localization technique for certain Noetherian rings like enveloping algebras of nilpotent Lie algebras. For such rings R we also give a conjectural definition of certain sheaves which should be "affine" objects naturally generalizing the classically defined structure sheaves in commutative theory. The corresponding sheaves associated to some R-modules might carry particularly interesting information; e.g., for representation theory of semisimple Lie groups. Next, we generalize one important theorem of P.F. Smith on localization in Noetherian Artin-Rees rings. As an interesting corollary we obtain that every prime ideal of height 1 in the enveloping algebra of the Lie algebra sl(2) over a field of characteristic zero is localizable. Finally, we provide a number of concrete useful calculations for our main example, the enveloping algebra of the three-dimensional Heisenberg Lie algebra; and thus test both the proposed ideas and methods. In particular, we introduce the notion of a weakly normal element, generalizing the notion of a normal element.

show abstract

Section: Introductionmentioning

confidence: 84%