TY - JOUR
T1 - Algebraic Geometry Over Algebraic Structures. VI. Geometrical Equivalence
AU - Daniyarova, E. Yu
AU - Myasnikov, A. G.
AU - Remeslennikov, V. N.
N1 - Publisher Copyright:
© 2017, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - The present paper is one in our series of works on algebraic geometry over arbitrary algebraic structures, which focuses on the concept of geometrical equivalence. This concept signifies that for two geometrically equivalent algebraic structures A and ℬ of a language L, the classification problems for algebraic sets over A and ℬ are equivalent. We establish a connection between geometrical equivalence and quasiequational equivalence.
AB - The present paper is one in our series of works on algebraic geometry over arbitrary algebraic structures, which focuses on the concept of geometrical equivalence. This concept signifies that for two geometrically equivalent algebraic structures A and ℬ of a language L, the classification problems for algebraic sets over A and ℬ are equivalent. We establish a connection between geometrical equivalence and quasiequational equivalence.
KW - algebraic structure
KW - geometrical equivalence
KW - prevariety
KW - quasivariety
KW - universal algebraic geometry
UR - http://www.scopus.com/inward/record.url?scp=85033406089&partnerID=8YFLogxK
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U2 - 10.1007/s10469-017-9449-2
DO - 10.1007/s10469-017-9449-2
M3 - Article
AN - SCOPUS:85033406089
SN - 0002-5232
VL - 56
SP - 281
EP - 294
JO - Algebra and Logic
JF - Algebra and Logic
IS - 4
ER -