Semifields - Open Access .click

AIP Conference Proceedings, 2020
A ternary partial semiring is a system consisting of an infinitary partial addition and a ternary multiplication satisfying a set of axioms. The set of nonpositive real numbers with respect to Σ, defined for countable support families of elements which are convergent and the usual ternary multiplication is a ternary partial semiring. In this paper, the
Siva Prasad Korrapati +2 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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On the Sporadic Semifield Flock

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 \(B\).
CARDINALI I, POLVERINO O, TROMBETTI, ROCCO +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.
EBERT G. +3 more
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