Algebraic Geometry over Algebraic Structures. VIII. Geometric Equivalences and Special Classes of Algebraic Structures

2021 ◽  
Vol 257 (6) ◽  
pp. 797-813
Author(s):  
E. Yu. Daniyarova ◽  
A. G. Myasnikov ◽  
V. N. Remeslennikov
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Structures ◽  
Special Classes

Pullback of the Normal Module of Ideals with Low Codimension

2021 ◽  
Author(s):  
Cleto B Miranda-Neto
Keyword(s):  
Algebraic Geometry ◽  
Commutative Algebra ◽  
Difficult Problem ◽  
Natural Projection ◽  
Analytic Spread ◽  
Reduction Number ◽  
Numerical Invariants ◽  
Special Classes

Abstract The normal module (or sheaf) of an ideal is a celebrated object in commutative algebra and algebraic geometry. In this paper, we prove results about its pullback under the natural projection, focusing on subtle numerical invariants such as, for instance, the reduction number. For certain codimension 2 perfect ideals, we show that the pullback has reduction number two. This is of interest since the determination of this invariant in the context of modules (even for special classes) is a mostly open, difficult problem. The analytic spread is also computed. Finally, for codimension 3 Gorenstein ideals, we determine the depth of the pullback, and we also consider a broader class of ideals provided that the Auslander transpose of the conormal module is almost Cohen–Macaulay.

Algebraic Geometry Over Algebraic Structures. IX. Principal Universal Classes and Dis-Limits

2019 ◽  
Vol 57 (6) ◽  
pp. 414-428
Author(s):  
E. Y. U. Daniyarova ◽  
A. G. Myasnikov ◽  
V. N. Remeslennikov
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Structures ◽  
Universal Classes

Algebraic geometry over algebraic structures. V. The case of arbitrary signature

2012 ◽  
Vol 51 (1) ◽  
pp. 28-40 ◽  
Author(s):  
E. Yu. Daniyarova ◽  
A. G. Myasnikov ◽  
V. N. Remeslennikov
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Structures ◽  
Arbitrary Signature

scholarly journals Algebraic geometry over algebraic structures. II. Foundations

2012 ◽  
Vol 185 (3) ◽  
pp. 389-416 ◽  
Author(s):  
E. Yu. Daniyarova ◽  
A. G. Myasnikov ◽  
V. N. Remeslennikov
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Structures

Algebraic geometry over algebraic structures X: Ordinal dimension

2018 ◽  
Vol 28 (08) ◽  
pp. 1425-1448
Author(s):  
Evelina Yur’evna Daniyarova ◽  
Alexei Georgievich Myasnikov ◽  
Vladimir Nikanorovich Remeslennikov
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Variety ◽  
Krull Dimension ◽  
Coordinate Ring ◽  
Algebraic Structures ◽  
Ordinal Numbers ◽  
Arbitrary Signature

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).

Algebraic geometry over algebraic structures. IV. Equational domains and codomains

2011 ◽  
Vol 49 (6) ◽  
pp. 483-508 ◽  
Author(s):  
É. Yu. Daniyarova ◽  
A. G. Myasnikov ◽  
V. N. Remeslennikov
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Structures

Algebraic geometry over algebraic structures. IX. Principal universal classes and Dis-limits

2017 ◽  
Vol 57 (6) ◽  
pp. 639-661
Author(s):  
E. Yu. Daniyarova ◽  
A. G. Myasnikov ◽  
V. N. Remeslennikov
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Structures ◽  
Universal Classes

Algebraic Geometry Over Algebraic Structures. VI. Geometrical Equivalence

2017 ◽  
Vol 56 (4) ◽  
pp. 281-294 ◽  
Author(s):  
E. Yu. Daniyarova ◽  
A. G. Myasnikov ◽  
V. N. Remeslennikov
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Structures
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