# Semifield

On this page:

## Definition of the noun Semifield

What does Semifield mean as a name of something?

**noun**

- [
*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

Click on a title to look inside that book (if available):

### 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

Click on a label to prioritize search results according to that topic:

## 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 S_{1}E_{1}M_{3}I_{1}F_{4}I_{1}E_{1}L_{1}D_{2}

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

## Share this page

## Next...

Go to the wordplay of Semifield for some fun with words!