TY - JOUR
T1 - On the geometric equivalence of algebras
AU - Shahryari, M.
N1 - Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2024/2/1
Y1 - 2024/2/1
N2 - It is known that an algebra is geometrically equivalent to any of its filterpowers if it is qω-compact. We present an explicit description for the radicals of systems of equation over an algebra A and then we prove the above assertion by an elementary new argument. Then we define qκ-compact algebras and κ-filterpowers for any infinite cardinal κ. We show that any qκ-compact algebra is geometric equivalent to its κ-filterpowers. As there is no algebraic description of the κ-quasivariety generated by an algebra, the classical argument can not be applied in this case, while our proof still works.
AB - It is known that an algebra is geometrically equivalent to any of its filterpowers if it is qω-compact. We present an explicit description for the radicals of systems of equation over an algebra A and then we prove the above assertion by an elementary new argument. Then we define qκ-compact algebras and κ-filterpowers for any infinite cardinal κ. We show that any qκ-compact algebra is geometric equivalent to its κ-filterpowers. As there is no algebraic description of the κ-quasivariety generated by an algebra, the classical argument can not be applied in this case, while our proof still works.
KW - Algebraic sets
KW - Algebraic structures
KW - Equations
KW - Filterpowers
KW - Geometric equivalence
KW - Quasi-identities
KW - Radical ideals
KW - q-compactness
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UR - https://www.mendeley.com/catalogue/552017e5-396a-3f4d-9d16-c687049c33fb/
U2 - 10.1016/j.apal.2023.103386
DO - 10.1016/j.apal.2023.103386
M3 - Article
AN - SCOPUS:85173980314
SN - 0168-0072
VL - 175
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 2
M1 - 103386
ER -