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Semifield

Definition of the noun Semifield

What does Semifield mean as a name of something?

noun

  1. [mathematics] An algebraic structure with two binary operations, addition and multiplication, similar to the field but with some axioms relaxed.

Explanation

Semifield: In mathematics, a semifield is an algebraic structure with two binary operations, addition and multiplication, which is similar to a field, but with some axioms relaxed. There are at least two conflicting conventions of what constitutes a semifield.

Printed books with definitions for Semifield

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Google previewSurveys in Combinatorics 2005 (2005)

by Bridget S. Webb

Semifield flocks, translation ovoids of Q(4,g), eggs and TGQ A semifield is a division algebra (not necessarily associative). The middle ...

Google previewAlgebraic Curves and Finite Fields (2014)

Cryptography and Other Applications by Harald Niederreiter, Alina Ostafe, Daniel Panario, Arne Winterhof

Roughly speaking, a semifield is a field without associativity for the multiplication. More precisely, a (finite) semifield is defined as follows. Definition 2.1. Let S be a finite set containing at least two elements. Then, S together with two binary ...

Google previewNon-Associative and Non-Commutative Algebra and Operator Theory (2016)

NANCAOT, Dakar, Senegal, May 23–25, 2014: Workshop in Honor of Professor Amin Kaidi by Cheikh Thiécoumbe Gueye, Mercedes Siles Molina

A semifield is a semiring with identity such that each non-zero element of S is invertible. Definition 17.1. Let S be a semiring. An element a of S is: • Additively cancellable in S if for all b;c 2 S then a C b D a C c implies b D c. • zero-sum if there ...

Google previewRelational and Algebraic Methods in Computer Science

by Peter Höfner, Damien Pous and Georg Struth

Idempotent Semifield An idempotent semifield is a system (X,0,1,⊕,⊗), where X is a nonempty set endowed with associative and commutative operations, addition ⊕ and multiplication ⊗, which have as neutral elements the zero 0 and the ...

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Video about Semifield

Semifield Meaning

Video shows what semifield means. An algebraic structure with two binary operations, addition and multiplication, similar to the field but with some axioms ...

Scrabble value of S1E1M3I1F4I1E1L1D2

The value of this 9-letter word is 15 points, but it's not an accepted word in the Official Scrabble Players Dictionary.

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