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Subrings of Generated by Monomials

Published online by Cambridge University Press:  20 November 2018

David F. Anderson
David F. Anderson*
Affiliation:
University of Tennessee, Knoxville, Tennessee
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In this paper we study subrings A of generated by monomials over . If A is normal and A ⊂ B integral, we can completely characterize A. If dim A = 2, we show that A is isomorphic to a subring A’ of B generated by monomials with A’ ⊂ B integral. The author became interested in these rings while studying projective modules over subrings of , For some applications, see [1].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 1 , 01 February 1978 , pp. 215 - 224
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Anderson, D. F., Projective modules over subrings of k[X, Y] generated by monomials, (submitted).Google Scholar
2. Bass, H., Algebraic K-theory (W. A. , New York, 1968).Google Scholar
3. Possum, R., The divisor class group of a Krull domain (Springer-Verlag, New York, 1973).Google Scholar
4. Hochster, M., Rings of invariants of tori, Cohen-AIacaulay rings generated by monomials, and poly topes, Ann. of Math. 96 (1972), 318–337.Google Scholar
5. Samuel, P., Unique factorization domains (Lecture notes), Tata Institute, Bombay; 1964.Google Scholar
6. Swan, R. G., Algebraic K-theory, Lecture notes in mathematics 76 (Springer, Berlin, 1968).Google Scholar
7. Waterhouse, W. C., Divisor classes in pseudo Galois extensions, Pac. J. Math. 36 (1971), 541–548.Google Scholar