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Near-rings with identities on dihedral groups

Published online by Cambridge University Press:  20 January 2009

Marjory J. Johnson
Marjory J. Johnson
Affiliation:
The University of South Carolina, Columbia, South Carolina 29208, United States of America
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Normal right submodules and right ideals need not coincide in an arbitrary near-ring. Berman and Silverman (1) have shown that in a near-ring (N, +, ·) with a two-sided zero (i.e. x · 0 = 0 · x = 0, for all x ∈ N) a right ideal is also a right submodule. If (N, +, ·) is in fact a distributively generated near-ring, then all normal right submodules are also right ideals. (See (5).)

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 3 , June 1973 , pp. 219 - 228
Copyright
Copyright © Edinburgh Mathematical Society 1973

References

REFERENCES

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