A Heyting field is one of the inequivalent ways in constructive mathematics to capture the classical notion of a field. It is essentially a field with...

Boolean algebras, Heyting algebras form a variety axiomatizable with finitely many equations. Heyting algebras were introduced by Arend Heyting (1930) to formalize...

Arend Heyting (Dutch: [ˈaːrənt ˈɦɛitɪŋ]; 9 May 1898 – 9 July 1980) was a Dutch mathematician and logician. Heyting was a student of Luitzen Egbertus Jan...

(1984), Chapter 3 Mines, Richman & Ruitenburg (1988), §II.2. See also Heyting field. Beachy & Blair (2006), p. 120, Ch. 3 Artin (1991), Chapter 13.4 Lidl...

ordered field is a field together with a total ordering of its elements that is compatible with the field operations. Basic examples of ordered fields are...

field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is...

the topology. Every Heyting algebra can be represented by a topological field of sets with the underlying lattice of the Heyting algebra corresponding...

In algebra, a division ring, also called a skew field (or, occasionally, a sfield), is a nontrivial ring in which division by nonzero elements is defined...

analysis. Constructive frameworks for its formulation are extensions of Heyting arithmetic by types including N N {\displaystyle {\mathbb {N} }^{\mathbb...

open elements of an interior algebra form a Heyting algebra and the closed elements form a dual Heyting algebra. The regular open elements and regular...

CD in 2006, Drentse dichters lezen: Hans Heyting, on which Drèents writers read poems by Heyting. Heyting's early dramatic work was received positively:...

and complex numbers. Scalars can also be, more generally, elements of any field. Vector spaces generalize Euclidean vectors, which allow modeling of physical...

in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer–Heyting–Kolmogorov interpretation) and Stephen Kleene (see...

In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic...

⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ algebraically closed fields Formally, a unique factorization domain is defined to be...

polynomials over a field K. For each nonzero polynomial P, define f (P) to be the degree of P. K[[X]], the ring of formal power series over the field K. For each...

Hilbert. Brouwer's ideas were subsequently taken up by his student Arend Heyting and Hilbert's former student Hermann Weyl. In addition to his mathematical...

whose integral closure in its field of fractions is A itself. Spelled out, this means that if x is an element of the field of fractions of A that is a root...

principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ algebraically closed fields Examples include: K {\displaystyle K} : any field, Z {\displaystyle \mathbb {Z} }...

infinity, as a Heyting algebra, is subdirectly representable as a subalgebra of the direct product of the finite linearly ordered Heyting algebras. The...

Examples: A graded vector space is an example of a graded module over a field (with the field having trivial grading). A graded ring is a graded module over itself...

vertical negation stroke. This negation symbol was reintroduced by Arend Heyting in 1930 to distinguish intuitionistic from classical negation. It also...

include Heyting and Boolean algebras. These lattice-like structures all admit order-theoretic as well as algebraic descriptions. The sub-field of abstract...

Domain Integral domain Field Division ring Lie ring Ring theory Lattice-like Lattice Semilattice Complemented lattice Total order Heyting algebra Boolean algebra...

⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ algebraically closed fields An integral domain is a nonzero commutative ring in which...

Boolean algebra Monadic Boolean algebra De Morgan algebra First-order logic Heyting algebra Lindenbaum–Tarski algebra Skew Boolean algebra Algebraic normal...

the definition: see below. A field is a commutative ring in which there are no nontrivial proper ideals, so that any field is a Dedekind domain, however...

Domain Integral domain Field Division ring Lie ring Ring theory Lattice-like Lattice Semilattice Complemented lattice Total order Heyting algebra Boolean algebra...

⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ algebraically closed fields Every irreducible element of a GCD domain is prime. A GCD...

applications involve the subclass of near-rings known as near-fields; for these see the article on near-fields. There are various applications of proper near-rings...