Results 1 to 10 of about 4,211 (96)
The group of automorphisms of a distributively generated near ring [PDF]
Proceedings of the American Mathematical Society, 1983 S. D. Scott has shown that the group of automorphisms of the near ring generated by the automorphisms of a given group is isomorphic to the automorphism group of the given group if that group’s automorphism is complete. Here that theorem is generalized by showing that the group of automorphisms of a near ring distributively generated by its units is a ...
J. Malone
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Prime ideals and the ideal-radical of a distributively generated near-ring [PDF]
Mathematische Zeitschrift, 1964 The concepts of a prime ideal of a distributively generated (d.g.) nearring R, a prime d.g. near-ring and an irreducible R-group are introduced1). The annihilating ideal of an irreducible R-group with an R-generator is a prime ideal. Consequently we define a prime ideal to be primitively prime if it is the annihilating ideal of such an R-group, and a d.
R. Laxton
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On distributively generated near-rings [PDF]
Proceedings of the Edinburgh Mathematical Society, 1969 The following theorems in ring theory are well-known:1. Let R be a ring. If e is a unique left identity, then e is also a right identity.2. If R is a ring with more than one element such that aR = R for every nonzero element a ε R, then R is a division ring.3. A ring R with identity e ≠ 0 is a division ring if and only if it has no proper right ideals.
Steve Lich
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On group distributively generated near-rings [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1992 AbstractThe group near-ring constructed from a right near-ring R and a group G is studied in the special case where the near-ring is distributively generated. In particular, results concerning homomorphisms of near-rings or of groups and the augmentation ideal are obtained which resemble closely those obtained for group rings.
R. Fray
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Division of distributively generated near-rings II [PDF]
Bulletin of the Australian Mathematical Society, 1987 The definition of division d.g. near-rings given by the author in 1976 has been found to be too restrictive. In this paper we generalise the definition of division d.g. near-rings and extend the results obtained earlier for division d.g. near-rings to the new wider class of near-rings.
V. Tharmaratnam
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Generalised quaternion groups and distributively generated near-rings [PDF]
Proceedings of the Edinburgh Mathematical Society, 1973 In this paper two major questions concerning generalised quaternion groups and distributively generated (d.g.) near-rings are investigated. The d.g. near-rings generated, respectively, by the inner automorphisms, automorphisms, and endomorphisms of the group are described. It is also shown that these morphism near-rings are local near-rings and contain
J. Malone
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Regular topological distributively generated near-rings [PDF]
Bulletin of the Australian Mathematical Society, 1987 In this paper we introduce regular topological distributively generated (d.g.) near-rings (distinct from d.g. regular near-rings) as the d.g. near-ring analogue of regular rings and develop a structure theory for this class of near-rings.
V. Tharmaratnam
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Residual finiteness and ‘free’ distributively generated near-rings [PDF]
Journal of the Australian Mathematical Society, 1979 AbstractLet V be a variety of groups in which the free group is residually finite, and let S be a residually finite semigroup. Let Nv(S) be the ‘free’ distributively generated near-ring constructed from S and V. Theorem; Nv(S) is residually finite.
David J. John
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Distributively Generated Centralizer Near-Rings [PDF]
Proceedings of the American Mathematical Society, 1983 Let G G be a finite group. A \mathcal {A} a group of automorphisms of G G and C ( A ; G ) \mathcal {C}\left ( {\mathcal {A};G} \right ) the ...
Maxson, C. J., Smith, K. C.
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Medial and distributively generated near-rings
Monatshefte f�r Mathematik, 1990 It is shown that fully invariant groups play a role in the structure of near-rings, especially in d.g. near-rings. Properties of these additive groups are then used to obtain results about d.g., medial, or subdirectly irreducible near-rings or about near-rings whose additive groups are locally nilpotent.
Birkenmeier, Gary, Heatherly, Henry
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