Prime Antiflexible Derivation Alternator Rings

Rao, Vartika; Suvarna, K.

doi:10.3923/aja.2010.1.7

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2023

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“…K.Suvarna, V.M. Rao [2] showed that a prime derivation alternator ring with (x, y, z) = (z, y, x) is either associative or N = C, the center. Bharathi and Munirathnam [3] proved that idempotent e lies in nucleus in a semi prime derivation alternator ring.…”

Section: Introductionmentioning

confidence: 99%

Alternative Derivations in (1,1) Rings

K. Subhashini,

M. Shiva Sankar Reddy,

V. Raghavendra Prasad

2023

J. Adv. Zool.

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Objectives: To show the associativity in one of the subclass of non-associative (γ,δ) rings. Method: Derivation alternator rings are limiting case of associative rings. The ring (1,1) is one of the sub class of (γ,δ) rings. Consider a (1,1) derivation alternator ring R, with characteristic ≠ 2, and it is well known that this ring is neither alternative nor flexible. In this paper it will be proved that right alternative property (R,x,x) holds in R and flexibility follows, finally associativity arrives in R. Findings: If this ring R does not contain nilpotent elements even though it will be associative. Novelty: Further investigators may extend the applications of these rings in science and engineering fields. Mathematics Subject Classification: 2010 MSC 17D

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Section: Introductionmentioning

confidence: 99%