TY - JOUR
T1 - Universal geometrical equivalence of the algebraic structures of common signature
AU - Daniyarova, E. Yu
AU - Myasnikov, A. G.
AU - Remeslennikov, V. N.
N1 - Publisher Copyright:
© 2017, Pleiades Publishing, Ltd.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - This article is a part of our effort to explain the foundations of algebraic geometry over arbitrary algebraic structures [1–8]. We introduce the concept of universal geometrical equivalence of two algebraic structures A and B of a common language L which strengthens the available concept of geometrical equivalence and expresses the maximal affinity between A and B from the viewpoint of their algebraic geometries. We establish a connection between universal geometrical equivalence and universal equivalence in the sense of equality of universal theories.
AB - This article is a part of our effort to explain the foundations of algebraic geometry over arbitrary algebraic structures [1–8]. We introduce the concept of universal geometrical equivalence of two algebraic structures A and B of a common language L which strengthens the available concept of geometrical equivalence and expresses the maximal affinity between A and B from the viewpoint of their algebraic geometries. We establish a connection between universal geometrical equivalence and universal equivalence in the sense of equality of universal theories.
KW - algebraic structure
KW - universal algebraic geometry
KW - universal class
KW - universal equivalence
KW - universal geometrical equivalence
UR - http://www.scopus.com/inward/record.url?scp=85032018682&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85032018682&partnerID=8YFLogxK
U2 - 10.1134/S003744661705007X
DO - 10.1134/S003744661705007X
M3 - Article
AN - SCOPUS:85032018682
SN - 0037-4466
VL - 58
SP - 801
EP - 812
JO - Siberian Mathematical Journal
JF - Siberian Mathematical Journal
IS - 5
ER -