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Semifield Metrizability

Semifield Metrizability
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On the Sporadic Semifield Flock [PDF]

Designs, Codes and Cryptography, 2003
Let \(Q(4,q)\) denote the parabolic quadric of \(\text{ PG}(4,q)\). An ovoid of \(Q(4,q)\) is a set of \(q^2+1\) points of \(Q(4,q)\) such that no two of them are collinear (on a line of \(Q(4,q)\)). A BLT-set \(B\) is a set of \(q+1\) points of \(Q(4,q)\) such that no point of \(Q(4,q)\) is collinear with more than two points of \(B\).
Ilaria Cardinali, Olga Polverino, Rocco Trombetti   +2 more
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Infinite families of new semifields

Combinatorica, 2009
The authors construct six new infinite families of finite semifields, all of which are two-dimensional over their left nuclei. The semifields are given by providing spread sets of linear mappings. It is shown that semifields in different families are never isotopic. The classification of isotopy classes within a given family is still ongoing.
Gary L. Ebert, Giuseppe Marino 0002, Olga Polverino, Rocco Trombetti   +3 more
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Algebraic extensions of semifields

Russian Mathematical Surveys, 2004
A semifield is a semiring \((D,+,\bullet)\) such that each nonzero element is invertible with repect to multiplication and is not invertible with respect to addition. In this paper, the author examines the possibility of extending a semifield by a root of an algebraic equation. Let \(D\) denote a semifield. Then \(D\) is called idempotent (cancellable)
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Semifields and their properties

Journal of Mathematical Sciences, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vechtomov, E. M., Cheraneva, A. V.
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Simplectic spreads and finite semifields

Designs, Codes and Cryptography, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Finite semifields

2011
About this title: Galois geometry is the theory that deals with substructures living in projective spaces over finite fields, also called Galois fields. This collected work presents current research topics in Galois geometry, and their applications. Presented topics include classical objects, blocking sets and caps in projective spaces, substructures ...
LAVRAUW M, POLVERINO, Olga
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Generalized semifields

A triple (S, +, · ) is said to be semiring iff S is a set and + and · are binary operations on S such that (1) (S,+) is a commutative semigroup, (2) (S, ·) is commutative semigroup, (3) (x+y) ·z=x·z+y·z for all x, y, z, ɛ , S. A semiring (D,+, ·) is said to be a ratio semiring iff (D, ·) is a group.
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Simple skew semifields and semifields

Siberian Mathematical Journal, 1974
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Symplectic semifield spreads of PG(5, q) and the veronese surface

Ricerche Di Matematica, 2010
G Lunardon, O Polverino, Rocco Trombetti   +2 more
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