Access the full text.
Sign up today, get DeepDyve free for 14 days.
References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.
THE GOLDIE CONDITIONS FOR ALGEBRAS WITH BOUNDED GROWTH RONALD S. IRVING AND LANCE W. SMALL 1. Introduction In this paper we consider possible generalizations of results of Jategaonkar and Bergman [6, 7] which state that a domain with no free subalgebras, or subexponential growth, has a division ring of fractions. Recall for an algebra A generated over a field K by a finite set X that the growth function of A with respect to X is the function f :N -+ N with f(n) equal to the dimension of the space spanned by all monomials on X of length ^ n. If / is bounded by a polynomial, A is said to have polynomially bounded growth, and if / grows exponentially, A has 1/ n exponential growth. More precisely, A has exponential growth if lim/(n) > 1; otherwise A has subexponential growth. In case A has polynomially bounded growth, the infimum of degrees of functions n bounding / is the Gelfand-Kirillov dimension of A; it is independent of the choice of X. For algebras A which are not finitely-generated, these terms still apply via a consideration of all finitely-generated subalgebras. The striking results of Jategaonkar and Bergman suggest that
Bulletin of the London Mathematical Society – Wiley
Published: Nov 1, 1983
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.