Regular Near-Rings

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Authors

  • University of Southwestern Louisiana, Lafayette, Louisiana ,US

Abstract

The concept of a regular near-ring was introduced in 1968 by J.C. Beidleman [1]. Strictly analogous to the ring theoretic concept we say a (left) near-ring R is von Neumann regular (or for simplicity, regular) if for each x ∈ R there exists x' ∈ R such that xx'x = x. Ligh [8] was the first to give some structure theory for regular near-rings.

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Published

1974-12-01

How to Cite

Heatherly, H. E. (1974). Regular Near-Rings. The Journal of the Indian Mathematical Society, 38(1-4), 345–354. Retrieved from http://informaticsjournals.com/index.php/jims/article/view/16710

 

References

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D.W. BLACKETT, The near-ring of affine transformations, Proe. Amer. Math. Soc. 7 (1956), 517-519.

J.R. CLAY, The near-rings on groups of low order, Math. Z. 104 (1968), 364-371.

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H.E. HEATHERLY, C-Z transitivity and C-Z decomposable near-rings, J. Alg. 19 (1971), 496-508.

R.R. LAXTON, Primitive distributively generated near-rings, Mathematika 8 (1961), 143-158.

STEVE UGH, On regular near-rings, Math. Japonicae, 15 (1970), 7-13.

STEVE LIGH, On commutativity of near-rings, Kyungpook Math. J. 10 (1970), 105-106.

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J.J. MALONE AND H.E. HEATHERLY, Some near-ring embeddings, Quart. J. Math. Oxford (2) 20 (1969), 81-85.

J.J. MALONE, A near-ring analogue of a ring embedding theorem, J. Alg. 16 (1970), 237-238.

N. MCCOY, The theory of rings, Macmillan, New York, 1966.

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K.G. WOLFSON, Two-sided ideals of the affine near-ring, Amer, Math. Monthly 65 (1958), 29-30.