On the notion of Krull super-dimension

A. Masuoka; A. N. Zubkov

doi:10.1016/j.jpaa.2019.106245

On the notion of Krull super-dimension

A. Masuoka
, A. N. Zubkov

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We introduce the notion of Krull super-dimension of a super-commutative super-ring. This notion is used to describe regular super-rings and calculate Krull super-dimensions of completions of super-rings. Moreover, we use this notion to introduce the notion of super-dimension of any irreducible superscheme of finite type. Finally, we describe nonsingular superschemes in terms of sheaves of Kähler superdifferentials.

Original language	English
Article number	106245
Journal	Journal of Pure and Applied Algebra
Volume	224
Issue number	5
DOIs	https://doi.org/10.1016/j.jpaa.2019.106245
Publication status	Published - May 2020

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2019.106245

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abstract = "We introduce the notion of Krull super-dimension of a super-commutative super-ring. This notion is used to describe regular super-rings and calculate Krull super-dimensions of completions of super-rings. Moreover, we use this notion to introduce the notion of super-dimension of any irreducible superscheme of finite type. Finally, we describe nonsingular superschemes in terms of sheaves of K{\"a}hler superdifferentials.",

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AB - We introduce the notion of Krull super-dimension of a super-commutative super-ring. This notion is used to describe regular super-rings and calculate Krull super-dimensions of completions of super-rings. Moreover, we use this notion to introduce the notion of super-dimension of any irreducible superscheme of finite type. Finally, we describe nonsingular superschemes in terms of sheaves of Kähler superdifferentials.

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On the notion of Krull super-dimension

Abstract

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