When is the SIP (SSP) property inherited by free modules
A right R-module M has right SIP (SSP) if the intersection (sum) of two direct summands of M is also a direct summand. It is shown that the right SIP (SSP) is not a Morita invariant property and that a nonsingular C(11)(+)-module does not necessarily have SIP. In contrast, it is shown that the direc...
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| Veröffentlicht in: | Acta mathematica Hungarica 2006-07, Vol.112 (1-2), p.103-106 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | A right R-module M has right SIP (SSP) if the intersection (sum) of two direct summands of M is also a direct summand. It is shown that the right SIP (SSP) is not a Morita invariant property and that a nonsingular C(11)(+)-module does not necessarily have SIP. In contrast, it is shown that the direct sum of two copies of a right Ore domain has SIP as a right module over itself. |
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| ISSN: | 0236-5294 1588-2632 |
| DOI: | 10.1007/s10474-006-0067-z |