caa a22 4500 386307091 CHVBK 20180307111533.0 cr unu---uuuuu 161130e198804 xx s 000 0 eng 10.1017/S1446788700029827 doi S1446788700029827 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700029827 Hill David A. Instituto de Matematica Universidade Federal de Bahia Salvador, Bahia Brasil Injective Modules Over Non-Artinian Serial Rings [Elektronische Daten] [David A. Hill] A module is uniserial if its lattice of submodules is linearly ordered, and a ring R is left serial if R is a direct sum of uniserial left ideals. The following problem is considered. Suppose the injective hull of each simple left R-module is uniserial. When does this imply that the indecomposable injective left R-modules are uniserial? An affirmative answer is known when R is commutative and when R is Artinian. The following result is proved. Let R be a left serial ring and suppose that for each primitive idempotent e, eRe has indecomposable injective left modules uniserial. The following conditions are equivalent. (a) The injective hull of each simple left R-module is uniserial. (b) Every indecomposable injective left R-module is univerial. (c) Every finitely generated left R-module is serial. The rest of the paper is devoted to a study of some non-Artinian serial rings which serve to illustrate this theorem. Copyright © Australian Mathematical Society 1988 primary 16 A 52 nationallicence 16 A 53 nationallicence secondary 16 A 04 nationallicence Journal of the Australian Mathematical Society Cambridge University Press 44/2(1988-04), 242-251 1446-7887 44:2<242 1988 44 JAZ https://doi.org/10.1017/S1446788700029827 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700029827 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hill David A. Instituto de Matematica Universidade Federal de Bahia Salvador, Bahia Brasil NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 44/2(1988-04), 242-251 1446-7887 44:2<242 1988 44 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge