What does semifield mean?
Definitions for semifield
semi·field
This dictionary definitions page includes all the possible meanings, example usage and translations of the word semifield.
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Wiktionary
semifieldnoun
An algebraic structure with two binary operations, addition and multiplication, similar to the field but with some axioms relaxed.
Wikipedia
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.
Wikidata
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. ⁕In projective geometry and finite geometry, a semifield is the analogue of a division algebra, but defined over the integers Z rather than over a field. More precisely, it is a Z-algebra whose nonzero elements form a loop under multiplication. In other words, a semifield is a set S with two operations + and ·, such that ⁕ is an abelian group, ⁕multiplication is distributive on both the left and right, ⁕there exists a multiplicative identity element, and ⁕division is always possible: for every a and every nonzero b in S, there exist unique x and y in S for which b·x = a and y·b = a. ⁕In ring theory, combinatorics, functional analysis, and theoretical computer science, a semifield is a semiring in which all elements have a multiplicative inverse. These objects are also called proper semifields. A variation of this definition arises if S contains an absorbing zero that is different from the multiplicative unit e, it is required that the non-zero elements be invertible, and a·0 = 0·a = 0. Since multiplication is associative, the elements of a semifield form a group. However, the pair is only a semigroup, i.e. additive inverse need not exist, or, colloquially, 'there is no subtraction'. Sometimes, it is not assumed that the multiplication is associative.
Numerology
Chaldean Numerology
The numerical value of semifield in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of semifield in Pythagorean Numerology is: 1
Translations for semifield
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- полуполеRussian
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"semifield." Definitions.net. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.definitions.net/definition/semifield>.
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