Some results on T-noncosingular modules

Rachid TRIBAK

Makale detayları

Some results on T-noncosingular modules

Yazarlar:

Rachid TRIBAK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2014 Vol.38 Issue 1, pp.29-39

Belge Tipi:

Makale

Yayın Tarihi:

5/2014

Belge Dili:

Türkçe

Document ID (Org No.):

2000747423

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

The notion of T-noncosingularity of a module has been introduced and studied recently. In this article, a number of new results of this property are provided. It is shown that over a commutative semilocal ring R such that Jac(R) is a nil ideal, every T-noncosingular module is semisimple. We prove that for a perfect ring R, the class of T-noncosingular modules is closed under direct sums if and only if R is a primary decomposable ring. Finitely generated T-noncosingular modules over commutative rings are shown to be precisely those having zero Jacobson radical. We also show that for a simple module S, E(S) \oplus S is T-noncosingular if and only if S is injective. Connections of T-noncosingular modules to their endomorphism rings are investigated.

 

The notion of T-noncosingularity of a module has been introduced and studied recently. In this article, a number of new results of this property are provided. It is shown that over a commutative semilocal ring R such that Jac(R) is a nil ideal, every T-noncosingular module is semisimple. We prove that for a perfect ring R, the class of T-noncosingular modules is closed under direct sums if and only if R is a primary decomposable ring. Finitely generated T-noncosingular modules over commutative rings are shown to be precisely those having zero Jacobson radical. We also show that for a simple module S, E(S) \oplus S is T-noncosingular if and only if S is injective. Connections of T-noncosingular modules to their endomorphism rings are investigated.

Makale detayları

Some results on T-noncosingular modules

Yazarlar:

Rachid TRIBAK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2014 Vol.38 Issue 1, pp.29-39

Belge Tipi:

Makale

Yayın Tarihi:

5/2014

Belge Dili:

Türkçe

Document ID (Org No.):

2000747423

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Small submodules

T-noncosingular modules

endomorphism rings

Sayı

Makale detayları

Some results on T-noncosingular modules

Yazarlar: Rachid TRIBAK

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2014 Vol.38 Issue 1, pp.29-39

Belge Tipi: Makale

Yayın Tarihi: 5/2014

Belge Dili: Türkçe

Document ID (Org No.): 2000747423

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Small submodules

T-noncosingular modules

endomorphism rings

Sayı

Yazarlar:

Rachid TRIBAK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2014 Vol.38 Issue 1, pp.29-39

Belge Tipi:

Makale

Yayın Tarihi:

5/2014

Belge Dili:

Türkçe

Document ID (Org No.):

2000747423

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098