When is the SIP (SSP) property inherited by free modules

G. F. Birkenmeier; F. Karabacak; A. Tercan

doi:10.1007/s10474-006-0067-z

When is the SIP (SSP) property inherited by free modules

G. F. Birkenmeier
, F. Karabacak
, A. Tercan

Division of Algebra and Number Theory

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	103-106
Number of pages	4
Journal	Acta Mathematica Hungarica
Volume	112
Issue number	1-2
DOIs	https://doi.org/10.1007/s10474-006-0067-z
Publication status	Published - Jul 2006

Keywords

C11-module
Summand intersection property
Summand sum property

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abstract = "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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AU - Karabacak, F.

AU - Tercan, A.

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KW - Summand sum property

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When is the SIP (SSP) property inherited by free modules

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Keywords

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