GPQ modules and generalized Armendariz modules

Liang ZHAO

Makale detayları

GPQ modules and generalized Armendariz modules

Yazarlar:

Liang ZHAO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.637-648

Belge Tipi:

Makale

Yayın Tarihi:

3/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747893

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

GPQ modules; quasi-Armendariz modules; p.q.-Baer modules; weak Armendariz modules

Özet:

 

Let MR be a right R-module.  We introduce the concept of  right generalized p.q.-Baer modules (or simply, right GPQ modules) to  extend the notion of right p.q.-Baer modules.  We study on the  relationship between the GPQ property of a module MR and various  quasi-Armendariz properties.  We prove that every right GPQ module is  a quasi-Armendariz module.  As a sequence, we obtain a general form of  some known results considering the p.q.Baer property of a ring, some  known results are extended.  Moreover, we prove that for the formal  triangular ring R constructed from a pair of rings S, T and a bimodule  SMT, R is weak Armendariz if and only if (1) S and T are weak  Armendariz rings.  (2) SM and MT are weak Armendariz as a left  S-module and right R-module.  (3) If s(x)s'(x)=t(x)t'(x)=0, then  s(x)M[x] \cap M[x]t'(x)=0.  This gives the relationship of weak  Armendarizness between R and S, T, SMT, which plays a very important  role in ring theory.

 

Let MR be a right R-module.  We introduce the concept of  right generalized p.q.-Baer modules (or simply, right GPQ modules) to  extend the notion of right p.q.-Baer modules.  We study on the  relationship between the GPQ property of a module MR and various  quasi-Armendariz properties.  We prove that every right GPQ module is  a quasi-Armendariz module.  As a sequence, we obtain a general form of  some known results considering the p.q.Baer property of a ring, some  known results are extended.  Moreover, we prove that for the formal  triangular ring R constructed from a pair of rings S, T and a bimodule  SMT, R is weak Armendariz if and only if (1) S and T are weak  Armendariz rings.  (2) SM and MT are weak Armendariz as a left  S-module and right R-module.  (3) If s(x)s'(x)=t(x)t'(x)=0, then  s(x)M[x] \cap M[x]t'(x)=0.  This gives the relationship of weak  Armendarizness between R and S, T, SMT, which plays a very important  role in ring theory.

Makale detayları

GPQ modules and generalized Armendariz modules

Yazarlar: Liang ZHAO

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.637-648

Belge Tipi: Makale

Yayın Tarihi: 3/2011

Belge Dili: Türkçe

Document ID (Org No.): 2000747893

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

GPQ modules; quasi-Armendariz modules; p.q.-Baer modules; weak Armendariz modules

Sayı

Yazarlar:

Liang ZHAO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.637-648

Belge Tipi:

Makale

Yayın Tarihi:

3/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747893

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098