Algebraic geometry over algebraic structures X: Ordinal dimension

Evelina Yur Evna Daniyarova; Alexei Georgievich Myasnikov; Vladimir Nikanorovich Remeslennikov

doi:10.1142/S0218196718400039

Algebraic geometry over algebraic structures X: Ordinal dimension

Evelina Yur Evna Daniyarova
, Alexei Georgievich Myasnikov
, Vladimir Nikanorovich Remeslennikov

Department of Mathematical Sciences

RAS - Sobolev Institute of Mathematics, Siberian Branch

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

Abstract

This work is devoted to interpretation of concepts of Zariski dimension of an algebraic variety over a field and of Krull dimension of a coordinate ring in algebraic geometry over algebraic structures of an arbitrary signature. Proposed dimensions are ordinal numbers (ordinals).

Original language	English
Pages (from-to)	1425-1448
Number of pages	24
Journal	International Journal of Algebra and Computation
Volume	28
Issue number	8
DOIs	https://doi.org/10.1142/S0218196718400039
State	Published - 1 Dec 2018

Keywords

Krull dimension
Partially ordered set
Zariski dimension
algebraic structure
coordinate algebra
irreducible algebraic set
ordinal number
projective dimension
radical dimension
universal algebraic geometry

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10.1142/S0218196718400039

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title = "Algebraic geometry over algebraic structures X: Ordinal dimension",

abstract = "This work is devoted to interpretation of concepts of Zariski dimension of an algebraic variety over a field and of Krull dimension of a coordinate ring in algebraic geometry over algebraic structures of an arbitrary signature. Proposed dimensions are ordinal numbers (ordinals).",

keywords = "Krull dimension, Partially ordered set, Zariski dimension, algebraic structure, coordinate algebra, irreducible algebraic set, ordinal number, projective dimension, radical dimension, universal algebraic geometry",

author = "Daniyarova, \{Evelina Yur Evna\} and Myasnikov, \{Alexei Georgievich\} and Remeslennikov, \{Vladimir Nikanorovich\}",

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doi = "10.1142/S0218196718400039",

language = "English",

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T2 - Ordinal dimension

AU - Daniyarova, Evelina Yur Evna

AU - Myasnikov, Alexei Georgievich

AU - Remeslennikov, Vladimir Nikanorovich

PY - 2018/12/1

Y1 - 2018/12/1

N2 - This work is devoted to interpretation of concepts of Zariski dimension of an algebraic variety over a field and of Krull dimension of a coordinate ring in algebraic geometry over algebraic structures of an arbitrary signature. Proposed dimensions are ordinal numbers (ordinals).

AB - This work is devoted to interpretation of concepts of Zariski dimension of an algebraic variety over a field and of Krull dimension of a coordinate ring in algebraic geometry over algebraic structures of an arbitrary signature. Proposed dimensions are ordinal numbers (ordinals).

KW - Krull dimension

KW - Partially ordered set

KW - Zariski dimension

KW - algebraic structure

KW - coordinate algebra

KW - irreducible algebraic set

KW - ordinal number

KW - projective dimension

KW - radical dimension

KW - universal algebraic geometry

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UR - https://www.scopus.com/pages/publications/85052614620#tab=citedBy

U2 - 10.1142/S0218196718400039

DO - 10.1142/S0218196718400039

M3 - Article

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VL - 28

SP - 1425

EP - 1448

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 8

ER -

Algebraic geometry over algebraic structures X: Ordinal dimension

Abstract

Keywords

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