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The maxit and minit of a ring

Published online by Cambridge University Press:  18 May 2009

R. E. Peinado  and
W. G. Leavitt
R. E. Peinado
Affiliation:
University of Iowa and University of Nebraska
W. G. Leavitt
Affiliation:
University of Iowa and University of Nebraska
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In a recent paper [2] one of the authors has introduced the concept of module type of a ring, for rings with unit. The object of this paper is to generalize this concept to arbitrary rings, without assuming the existence of a unit. This is easily accomplished for rings with one-sided unit, and we shall define the type of such a ring. Theorem 2.5 gives a relation between this type and the module type of [2], and permits the immediate extension of all results in [2] to rings with one-sided unit.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 3 , January 1966 , pp. 128 - 135
Copyright
Copyright © Glasgow Mathematical Journal Trust 1966

References

REFERENCES

1.Blair, R. E., Ideal lattices and the structure of a ring, Trans. Amer. Math. Soc. 75 (1953), 136–153.Google Scholar
2.Leavitt, W. G., The module type of a ring, Trans. Amer. Math. Soc. 103 (1962), 113–130.Google Scholar
3.Jacobson, N., Structure of rings, American Mathematical Society Colloquium Publications, Vol. 37 (Providence, R. I., 1956).Google Scholar