A Course in Constructive Algebra

1989 ◽  
Vol 73 (465) ◽  
pp. 272 ◽  
Author(s):  
Haya Freedman ◽  
R. Mines ◽  
F. Richman ◽  
W. Ruitenburg
Keyword(s):  
Constructive Algebra

A Course in Constructive Algebra. By R. Mines, F. Richman, and W. Ruitenberg

1990 ◽  
Vol 97 (4) ◽  
pp. 357-362
Author(s):  
Michael J. Beeson
Keyword(s):  
Constructive Algebra

scholarly journals Constructive Algebra Methods for the L2-Problem For Stable Linear Systems

1994 ◽  
Vol 27 (8) ◽  
pp. 185-190
Author(s):  
Bernard Hanzon ◽  
Jan M. Maciejowski
Keyword(s):  
Linear Systems ◽  
Constructive Algebra ◽  
Stable Linear

scholarly journals Some relations and subsets generated by principal consistent subset of semigroup with apartness

2002 ◽  
pp. 7-25 ◽  
Author(s):  
Abraham Romano
Keyword(s):  
Set Theory ◽  
Semigroup Theory ◽  
Left Zero ◽  
Constructive Mathematics ◽  
Algebraic Structures ◽  
Main Subject ◽  
Special Cases ◽  
Constructive Algebra ◽  
Consistent Subset ◽  
Semigroup With Apartness

The investigation is in the Constructive algebra in the sense of E. Bishop, F. Richman, W. Ruitenburg, D. van Dalen and A. S. Troelstra. Algebraic structures with apartness the first were defined and studied by A. Heyting. After that, some authors studied algebraic structures in constructive mathematics as for example: D. van Dalen, E. Bishop, P. T. Johnstone, A. Heyting, R. Mines, J. C. Mulvey, F. Richman, D. A. Romano, W. Ruitenburg and A. Troelstra. This paper is one of articles in their the author tries to investigate semugroups with apartnesses. Relation q on S is a coequality relation on S if it is consistent, symmetric and cotran-sitive; coequality relation is generalization of apatness. The main subject of this consideration are characterizations of some coequality relations on semigroup S with apartness by means od special ideals J(a) = {x E S : a# SxS}, principal consistent subsets C(a) = {x E S : x# SaS} (a E S) of S and by filled product of relations on S. Let S = (S, =, 1) be a semigroup with apartness. As preliminaries we will introduce some special notions, notations and results in set theory, commutative ring theory and semigroup theory in constructive mathematics and we will give proofs of several general theorems in semigroup theory. In the next section we will introduce relation s on S by (x, y) E s iff y E C(x) and we will describe internal filfulments c(s U s?1) and c(s ? s?1) and their classes A(a) = ?An(a) and K(a) = ?Kn(a) respectively. We will give the proof that the set K(a) is maximal strongly extensional consistent ideal of S for every a in S. Before that, we will analyze semigroup S with relation q = c(s U s?1 ) in two special cases: (i) the relation q is a band coequality relation on S : (ii) q is left zero band coequality relation on S. Beside that, we will introduce several compatible equality and coequality relations on S by sets A(a), An(a), K(a) and Kn(a).

scholarly journals Lorenzen and Constructive Mathematics

2021 ◽  
pp. 47-61
Author(s):  
Thierry Coquand
Keyword(s):  
Mathematical Logic ◽  
Measure Theory ◽  
Constructive Mathematics ◽  
Short Survey ◽  
Recent Developments ◽  
Constructive Algebra

Abstract The goal of this paper is to present a short survey of some of Lorenzen’s contributions to constructive mathematics, and its influence on recent developments in mathematical logic and constructive algebra. We also present some work in measure theory which uses these contributions in an essential way.

A course in constructive algebra

1988 ◽  
Vol 26 (02) ◽  
pp. 26-0974-26-0974
Keyword(s):  
Constructive Algebra

Constructive algebra methods for the L 2 -problem for stable linear systems

Automatica ◽  
1996 ◽  
Vol 32 (12) ◽  
pp. 1645-1657 ◽  
Author(s):  
Bernard Hanzon ◽  
Jan M. Maciejowski
Keyword(s):  
Linear Systems ◽  
Constructive Algebra ◽  
Stable Linear

The Ascending Tree Condition: Constructive Algebra Without Countable Choice

2003 ◽  
Vol 31 (4) ◽  
pp. 1993-2002 ◽  
Author(s):  
Fred Richman
Keyword(s):  
Constructive Algebra ◽  
Tree Condition

scholarly journals Generalized Spaces for Constructive Algebra

2021 ◽  
pp. 99-187
Author(s):  
Ingo Blechschmidt
Keyword(s):  
Constructive Algebra

scholarly journals A univalent formalization of the p-adic numbers

2015 ◽  
Vol 25 (5) ◽  
pp. 1147-1171 ◽  
Author(s):  
ÁLVARO PELAYO ◽  
VLADIMIR VOEVODSKY ◽  
MICHAEL A. WARREN
Keyword(s):  
Proof Assistant ◽  
The Coq Proof Assistant ◽  
Coq Proof Assistant ◽  
Constructive Algebra ◽  
Univalent Foundations

The goal of this paper is to report on a formalization of the p-adic numbers in the setting of the second author's univalent foundations program. This formalization, which has been verified in the Coq proof assistant, provides an approach to the p-adic numbers in constructive algebra and analysis.

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