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

Cebir ve Sayılar Teorisi Anabilim Dalı

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

11 Alıntılar (Scopus)

Özet

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.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	103-106
Sayfa sayısı	4
Dergi	Acta Mathematica Hungarica
Hacim	112
Basın numarası	1-2
DOI'lar	https://doi.org/10.1007/s10474-006-0067-z
Yayın durumu	Yayınlandı - Tem 2006

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10.1007/s10474-006-0067-z

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title = "When is the SIP (SSP) property inherited by free modules",

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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author = "Birkenmeier, \{G. F.\} and F. Karabacak and A. Tercan",

year = "2006",

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doi = "10.1007/s10474-006-0067-z",

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T1 - When is the SIP (SSP) property inherited by free modules

AU - Birkenmeier, G. F.

AU - Karabacak, F.

AU - Tercan, A.

PY - 2006/7

Y1 - 2006/7

N2 - 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.

AB - 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.

KW - C11-module

KW - Summand intersection property

KW - Summand sum property

UR - https://www.scopus.com/pages/publications/33746189555

U2 - 10.1007/s10474-006-0067-z

DO - 10.1007/s10474-006-0067-z

M3 - Article

AN - SCOPUS:33746189555

SN - 0236-5294

VL - 112

SP - 103

EP - 106

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1-2

ER -

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

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