In this paper we study the structure of a right Noetherian ring R of finite right global dimesion integral over a central subring C and satisfying the following condition: if V, W are irreducible right K-modules with rc(V) = rc(W) then prdim(K) = pràim(W). 1. Introduction. Let £ be a ring with a central subring C. We shall say that R is homologically homogeneous (horn, horn.) over C if (i) R is right Noetherian; (ii) R is integral over C; (iii) the right global (projective) dimension of R (denoted rtgldim(£)) is finite; and (iv) if V and M are irreducible right £-modules whose annihilators in C, namely rc(V) and rc(W), are equal then prdimR(K) = prdim^H7). (Here, prdimR(F) denotes the projective dimension of the £-module V.) This paper is devoted to the study of such rings. Examples of them include (a) commutative Noetherian rings of finite global dimension; (b) hereditary Noetherian rings integral over their centers with no Artinian ideals; (c) right Noetherian local rings of finite right global dimension which are integral over their centers; and (d) certain rings arising in the representation theory of semisimple Lie groups [2]. In addition, we show in §7 that polynomial rings over horn. horn, rings, and certain group rings, are horn. horn. Rings of type (c) were studied in [5] where we showed that their maximal ideals had rank equal to their grade, defined in terms of maximal lengths of C-sequences. We termed such rings C-Macaulay-a precise definition is given in §2-and showed in [5, §4] that they share many of the properties of commutative Cohen-Macaulay

No abstract

Abstract. In this paper we study the structure of a right Noetherian ring R of finite right global dimesion integral over a central subring C and satisfying the following condition:if V, W are irreducible right K-modules with rc(V) = rc(W) then prdim(K) = pràim(W).1. Introduction. Let £ be a ring with a central subring C. We shall say that R is homologically homogeneous (horn, horn.) over C if (i) R is right Noetherian; (ii) R is integral over C; (iii) the right global (projective) dimension of R (denoted rtgldim(£)) is finite; and (iv) if V and M are irreducible right £-modules whose annihilators in C, namely rc(V) and rc(W), are equal then prdimR(K) = prdim^H7). . In addition, we show in §7 that polynomial rings over horn. horn, rings, and certain group rings, are horn. horn.Rings of type (c) were studied in [5] where we showed that their maximal ideals had rank equal to their grade, defined in terms of maximal lengths of C-sequences. We termed such rings C-Macaulay-a precise definition is given in §2-and showed in [5, §4] that they share many of the properties of commutative Cohen-Macaulay

No abstract