caa a22 4500 386360847 CHVBK 20180307111914.0 cr unu---uuuuu 161130e198904 xx s 000 0 eng 10.1017/S0004972700002689 doi S0004972700002689 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700002689 Teply Mark L. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53209, United States of America Global dimensions of right coherent rings with left Krull dimension [Elektronische Daten] [Mark L. Teply] The weak global dimension of a right coherent ring with left Krull dimension α ≥ 1 is found to be the supremum of the weak dimensions of the β-critical cyclic modules, where β < α. If, in addition, the mapping I → assl gives a bijection between isomorphism classes on injective left R-modules and prime ideals of R, then the weak global dimension of R is the supremum of the weak dimensions of the simple left R-modules. These results are used to compute the left homological dimension of a right coherent, left noetherian ring. Some analogues of our results are also given for rings with Gabriel dimension. Copyright © Australian Mathematical Society 1989 Bulletin of the Australian Mathematical Society Cambridge University Press 39/2(1989-04), 215-223 0004-9727 39:2<215 1989 39 BAZ https://doi.org/10.1017/S0004972700002689 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700002689 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Teply Mark L. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53209, United States of America NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 39/2(1989-04), 215-223 0004-9727 39:2<215 1989 39 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge