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T-Ideals and C-Ideals

Published online by Cambridge University Press:  20 January 2009

Aaron Klein
Aaron Klein
Affiliation:
Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel
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Given a ring R we consider the category Ŕ of R-rings (rings A with given ring-homomorphisms R → A), and R-homomorphisms (ring-homomorphisms that form commutative triangles with the given maps from R). All rings are associative and have 1, all homomorphisms send 1 to 1.

We define a c-R-ring as an object A in Ŕ with a family of maps {ρx ∈ homŔ(A,A)|x∈A}. Equivalently, a c-R-ring is an R-ring A with a binary operation a · b(= aρb) on A satisfying

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 2 , June 1979 , pp. 87 - 89
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

(1) Procesi, C., Rings with polynomial identities (M. Dekker, N.Y., 1973).Google Scholar
(2) Specht, W., Gesetze in Ringen 1, Mat. Zeit. 52 (1950), 557–589.CrossRefGoogle Scholar