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The kernel relation for a strict extension of certain regular semigroups

Published online by Cambridge University Press:  18 May 2009

Mario Petrich
Mario Petrich
Affiliation:
c/o J. E. Mills, Department of Mathematics, Seattle University, Seattle Washington 98122, USA
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Let R be a regular semigroup and denote by (R) its congruence lattice. For , the kernel of pis the set ker . The relation K on (R) defined by λKp if ker λ = ker p is the kernel relation on (R). In general, K is a complete ∩-congruence but it is not a v-congruence. In view of the importance of the kernel-trace approach to the study of congruences on a regular semigroup (the trace of p is its restriction to idempotents of R), it is of considerable interest to determine necessary and sufficient conditions on R in order for K to be a congruence. This being in general a difficult task, one restricts attention to special classes of regular semigroups. For a background on this subject, consult [1].

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 3 , September 1996 , pp. 347 - 357
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

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