On dimension theory of supermodules, super-rings, and superschemes

A. N. Zubkov, P. S. Kolesnikov

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce the notion of Krull super-dimension of supermodules over certain super-commutative Noetherian super-rings. We investigate how this notion relates to the notion of odd regular sequence due T. Schmitt and how it behaves with respect to the transition to the graded and bigraded super-modules and super-rings associated with the original ones. We also apply these results to the super-dimension theory of superschemes of finite type and their morphisms.

Original languageEnglish
JournalCommunications in Algebra
DOIs
Publication statusAccepted/In press - 2022

Keywords

  • Fiber of superscheme morphism
  • Krull super-dimension
  • super-commutative Noetherian super-ring
  • supermodule
  • superscheme of finite type

ASJC Scopus subject areas

  • Algebra and Number Theory

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