Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T01:16:46.812Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on strongly regular near-rings

Published online by Cambridge University Press:  20 January 2009

Motoshi Hongan
Motoshi Hongan
Affiliation:
Tsuyama College of Technology, Numa, Tsuyama, Okayama, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let S be a semigroup. An element a of S is called right (resp. left) regular if a=a2x (resp. a=xa2) for some x∈S. If a is regular and right (resp. left) regular, a is called strongly right (resp. left) regular. As is well known, if a is strongly regular (i.e., right and left regular) then it is regular, more precisely, there exists uniquely an element x such that a= a2x,x= x2a and ax=xa, and a is contained in a subgroup of S (and conversely).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 3 , October 1986 , pp. 379 - 381
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

REFERENCES

1.Hirano, Y., Some studies on strongly π-regular rings, Math. J. Okayama Univ. 20 (1978), 141–149.Google Scholar
2.Petrich, M., Introduction to semigroups (Merrill, Columbus, Ohio, 1973).Google Scholar
3.Reddy, Y. V. and Murty, C. V. L. N., On strongly regular near-rings, Proc. Edinburgh Math. Soc. 27 (1984), 61–64.CrossRefGoogle Scholar