Open AccessPoint count divisibility for algebraic sets over ℤ/𝕡^{ℓ}ℤ and other finite principal rings
Author(s) -
Daniel J. Katz
Publication year - 2009
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-09-10017-5
Subject(s) - algorithm , artificial intelligence , computer science
We determine the greatest common divisor of the cardinalities of the algebraic sets generated by collections of polynomials f 1 , … , f t f_1,\ldots ,f_t of specified degrees d 1 , … , d t d_1,\ldots ,d_t in n n variables over a finite principal ring R R . This generalizes the theorems of Ax ( t = 1 t=1 , R R a field), N. M. Katz ( t t arbitrary, R R a field), and Marshall-Ramage ( t = 1 t=1 , R R an arbitrary finite principal ring).