On matrix rings with the SIP and the Ads

Figen Takil MUTLU

Makale detayları

On matrix rings with the SIP and the Ads

Yazarlar:

Figen Takil MUTLU

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2657-2663

Belge Tipi:

Makale

Yayın Tarihi:

9/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745788

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

In this paper, matrix rings with the summand intersection property (SIP) and the absolute direct summand (ads) property (briefly, SASASA) are studied.  A ring RRR has the right  SIP if the intersection of two direct summands of RRR is also a direct summand.  A right RRR-module MMM has the ads property  if for every decomposition  M=A⊕BM=A⊕BM=A\oplus B of MMM and every complement CCC of AAA in MMM, we have M=A⊕CM=A⊕CM=A\oplus C.    It is shown that  the trivial extension of RRR by MMM has the SA if and only if RRR has the SA, MMM has the ads, and (1−e)Me=0(1−e)Me=0(1-e)Me=0 for each idempotent eee in RRR.  It is also shown with an example that the SA is not a Morita invariant property.

Makale detayları

On matrix rings with the SIP and the Ads

Yazarlar: Figen Takil MUTLU

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2657-2663

Belge Tipi: Makale

Yayın Tarihi: 9/2018

Belge Dili: Türkçe

Document ID (Org No.): 2000745788

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Figen Takil MUTLU

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2657-2663

Belge Tipi:

Makale

Yayın Tarihi:

9/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745788

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098