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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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### Surveys 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 ...

### Algebraic 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 ...

### Non-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 ...

### Relational 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 ...

## Online dictionaries and encyclopedias with entries for Semifield

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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.