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Near-rings of quotients of endomorphism near-rings

Published online by Cambridge University Press:  20 January 2009

Michael Holcombe
Michael Holcombe
Affiliation:
Queen's University of Belfast
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Let be a category with finite products and a final object and let X be any group object in . The set of -morphisms, (X, X) is, in a natural way, a near-ring which we call the endomorphism near-ring of X in Such nearrings have previously been studied in the case where is the category of pointed sets and mappings, (6). Generally speaking, if Γ is an additive group and S is a semigroup of endomorphisms of Γ then a near-ring can be generated naturally by taking all zero preserving mappings of Γ into itself which commute with S (see 1). This type of near-ring is again an endomorphism near-ring, only the category is the category of S-acts and S-morphisms (see (4) for definition of S-act, etc.).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 4 , September 1975 , pp. 345 - 352
Copyright
Copyright © Edinburgh Mathematical Society 1975

References

REFERENCES

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