near ring

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near ring

[¦nir ¦riŋ]
(mathematics)
An algebraic system with two binary operations called multiplication and addition; the system is a group (not necessarily commutative) relative to addition, and multiplication is associative, and is left-distributive with respect to addition, that is, x (y + z) = xy + xz for any x, y, and z in the near ring.
References in periodicals archive ?
Davvaz defined qk -fuzzy sub nearrings and ideals of a nearring in [14].
0 1 2 3 a b c d 0 0 0 0 0 0 0 0 0 1 0 1 2 3 a b c d 2 0 2 0 2 2 2 0 0 3 0 3 2 1 b a c d a 0 a 2 b a b c d b 0 b 2 a b a c d c 0 c 0 c 0 0 0 0 d 0 d 0 d 2 2 0 0 Then (N, +,.) is a near-ring (see (2), Library Nearring (8/2, 857)).
N is called an S near-ring or an S' nearring according as x [member of] Nx or x [member of] xN for all x [member of] N.
Agboola, Introduction to Neutrosophic nearrings, Annals of Fuzzy Mathematics and Informatics, 12 (3) (2016) 397-410.
From a July 2015 international conference in Manipal, India, 25 papers examine the phenomena of nearrings and nearfields in algebra, with a particular focus on their relationship to geometry.
On constructing codes from planar nearrings. http://www.algebra.uni-linz.
Some of them in particular, nearrings and several kinds of semirings have been proven very useful.
Meera, Fuzzy soft prime ideals over right tenary nearrings, International Journal of Pure and Applied Mathematics, 85(3), (2013), 507-529.