On Baker's Finite Basis Theorem for Congruence Distributive Varieties

1979 ◽  
Vol 73 (2) ◽  
pp. 141 ◽  
Author(s):  
Stanley Burris
Keyword(s):  
Finite Basis ◽  
Basis Theorem ◽  
Congruence Distributive

scholarly journals A proof of Lyndon's finite basis theorem

1980 ◽  
Vol 29 (3) ◽  
pp. 229-233 ◽  
Author(s):  
Joel Berman
Keyword(s):  
Finite Basis ◽  
Basis Theorem

Integer points on curves of genus 1

1970 ◽  
Vol 67 (3) ◽  
pp. 595-602 ◽  
Author(s):  
A. Baker ◽  
J. Coates
Keyword(s):  
Finite Number ◽  
Finite Basis ◽  
Rational Approximations ◽  
Algebraic Numbers ◽  
Integer Points ◽  
Basis Theorem

1. Introduction. A well-known theorem of Siegel(5) states that there exist only a finite number of integer points on any curve of genus ≥ 1. Siegel's proof, published in 1929, depended, inter alia, on his earlier work concerning rational approximations to algebraic numbers and on Weil's recently established generalization of Mordell's finite basis theorem. Both of these possess a certain non-effective character and thus it is clear that Siegel's argument cannot provide an algorithm for determining all the integer points on the curve. The purpose of the present paper is to establish such an algorithm in the case of curves of genus 1.

An extension of Willard?s Finite Basis Theorem: Congruence meet-semidistributive varieties of finite critical depth

2005 ◽  
Vol 52 (2-3) ◽  
pp. 289-302 ◽  
Author(s):  
Kirby A. Baker ◽  
George F. McNulty ◽  
Ju Wang
Keyword(s):  
Finite Basis ◽  
Critical Depth ◽  
Basis Theorem

scholarly journals A finite basis theorem for residually finite, congruence meet-semidistributive varieties

2000 ◽  
Vol 65 (1) ◽  
pp. 187-200 ◽  
Author(s):  
Ross Willard
Keyword(s):  
Finite Algebra ◽  
Finite Basis ◽  
Finitely Based ◽  
Mal’Cev Condition ◽  
Residually Finite ◽  
Basis Theorem ◽  
Finite Language

AbstractWe derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then it is finitely based. Theorem B: there is an algorithm which, given m < ω and a finite algebra in a finite language, determines whether the variety generated by the algebra is congruence meet-semidistributive and residually less than m.

Finite basis theorem for varieties with a two-term identity

1978 ◽  
Vol 17 (6) ◽  
pp. 458-472 ◽  
Author(s):  
Yu. A. Medvedev
Keyword(s):  
Finite Basis ◽  
Basis Theorem

Mordell's finite basis theorem revisited

1986 ◽  
Vol 100 (1) ◽  
pp. 31-41 ◽  
Author(s):  
J. W. S. Cassels
Keyword(s):  
Algebraic Geometry ◽  
Finite Basis ◽  
Great Work ◽  
Rational Solutions ◽  
The Third ◽  
Basis Theorem ◽  
Theory Of Numbers

0. Mordell proved his ‘Finite Basis Theorem’ in the paper [31] ‘On the rational solutions of the indeterminate equations of the third and fourth degrees’ which appeared in 1922 in Volume 21 of these Proceedings. It had been assumed, rather than conjectured, by Poincaré some 20 years previously, but it was not what he had set out to prove. The theorem and its generalizations are at the heart of many of the most interesting achievements and problems of the theory of numbers and also of algebraic geometry. Mordell himself had virtually no part in these developments: his great work was to lie elsewhere ([5]).

scholarly journals Sets of integers closed under affine operators—the finite basis theorem

1979 ◽  
Vol 83 (1) ◽  
pp. 135-144 ◽  
Author(s):  
Dean Hoffman ◽  
David Klarner
Keyword(s):  
Finite Basis ◽  
Basis Theorem
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