TY  - JOUR
AB  - In her paper [3], Osofsky exhibited an example of a ring R containing 16 elements which (i) is equal to its left complete ring of quotients, (ii) is not self-injective and (iii) whose injective hull HR = H(RR) allows a ring structure extending the R-module structure of HR. In the present note, we offer a general method of constructing such rings; in particular, given a non-trivial split Frobenius algebra A and a natural n more or equal 2, a certain ring of n x n matrices over A provides such an example. Here, taking for A the semi-direct extension of Z/2Z by itself and n = 2, one gets the example of Osofsky. Thus, our approach answers her question on finding a non-computational method for proving the existence of such rings.
DA  - 1973
DO  - 10.1017/S1446788700013860
LA  - eng
IS  - 01
M2  - 7
PY  - 1973
SN  - 1446-7887
SP  - 7-13
T2  - The journal of the Australian Mathematical Society
TI  - A construction of rings whose injective hulls allow a ring structure
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-17817669
Y2  - 2024-11-22T01:18:12
ER  -