Journal article
ON SEMI-PRIMARY SELF-INJECTIVE RINGS AND FAITH'S QUASI-FROBENIUS CONJECTURE
Proceedings of the Edinburgh Mathematical Society, Vol.58(1), pp.219-229
02/01/2015
DOI: 10.1017/S0013091514000443
Abstract
A long-standing conjecture of Faith in ring theory states that a left self-injective semi-primary ring A is necessarily a quasi-Frobenius ring. We propose a new method for approaching this conjecture, and prove it under some mild conditions; we show that if the simple A-modules are at most countably generated over a subring of the centre of A, then the conjecture holds. Also, the conjecture holds for K algebras A over sufficiently large fields, i.e. if the cardinality of K is larger than the dimension of the simple A-modules (or of A/Jac(A)). This effectively proves the conjecture in many situations, and we obtain several previously known results on this problem as a consequence.
Details
- Title: Subtitle
- ON SEMI-PRIMARY SELF-INJECTIVE RINGS AND FAITH'S QUASI-FROBENIUS CONJECTURE
- Creators
- M. C Iovanov - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Proceedings of the Edinburgh Mathematical Society, Vol.58(1), pp.219-229
- Publisher
- CAMBRIDGE UNIV PRESS
- DOI
- 10.1017/S0013091514000443
- ISSN
- 0013-0915
- eISSN
- 1464-3839
- Number of pages
- 11
- Grant note
- POSDRU/89/1.5/S/58852 / European Social Fund within the Sectorial Operational Program Human Resources Development
- Language
- English
- Date published
- 02/01/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9984240777902771
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