TY - JOUR
T1 - On the notion of Krull super-dimension
AU - Masuoka, A.
AU - Zubkov, A. N.
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2020/5
Y1 - 2020/5
N2 - 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.
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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U2 - 10.1016/j.jpaa.2019.106245
DO - 10.1016/j.jpaa.2019.106245
M3 - Article
AN - SCOPUS:85073730540
SN - 0022-4049
VL - 224
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 5
M1 - 106245
ER -