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On Quotient Loops of Normal Subloops

Published online by Cambridge University Press:  20 November 2018

C. Santhakumari
C. Santhakumari*
Affiliation:
Department of Mathematics, Nagarjuna University, Nagarjunanagar, 522 510 Andhra Pradesh, India
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The following result is due to Wielandt [1, Lemma 2.9]: Let A, B, K be N-submodules of some N-module, where N is a zero symmetric near-ring. Then the N-module, Γ: = (A + K) ∩ (B + K) | (A ∩ B) + K is commutative. Using this result Wielandt obtained density theorem for 2-primitive near-rings with identity. Betsch [1] used Wielandt's result to obtain the density theorem for O-primitive near-rings. The purpose of this paper is to extend this result for loops.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 4 , 01 December 1979 , pp. 517 - 518
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Betsch, G., Primitive near-rings, Math, z, 130, 351-461 (1973).Google Scholar
2. Bruck, Hubert R., A survey of binary systems, Springer-Verlag, New York, Inc, 1966.Google Scholar