Symmetric modules over their endomorphism rings

Burcu Ungor, Yosum Kurtulmaz, Sait Halicioglu, Abdullah Harmanci

Abstract


Let \(R\) be an arbitrary ring with identity and \(M\) a right
\(R\)-module with \(S=End_R(M)\). In this paper, we study right
\(R\)-modules \(M\) having the property for \(f,g \in End_R(M)\) and
for \(m\in M\), the condition \(fgm = 0\) implies \(gfm = 0\). We prove
that some results of symmetric rings can be extended to symmetric
modules for this general setting.

Keywords


symmetric modules, reduced modules, rigid modules, semicommutative modules, abelian modules, Rickart modules, principally projective modules

Full Text:

PDF

References


N. Agayev, G. Güngöroğlu, A. Harmanci and S. Halicioglu, Abelian modules, Acta

Math. Univ. Comenianae 78(2)(2009), 235-244.

N. Agayev, S. Halicioglu and A. Harmanci, On symmetric modules, Riv. Mat.

Univ. Parma 8(2)(2009), 91-99.

N. Agayev, S. Halicioglu and A. Harmanci, On reduced modules, Commun. Fac.

Sci. Univ. Ank. Series A1 58(1)(2009), 9-16.

N. Agayev, S. Halicioglu and A. Harmanci, On Rickart modules, Bull. Iran. Math.

Soc. 38(2)(2012), 433-445.

D. D. Anderson and V. Camillo, Semigroups and rings whose zero products

commute, Comm. Algebra 27(6)(1999), 2847-2852.

A. W. Chatters and C. R. Hajarnavis, Rings with chain conditions, Pitman, Boston,

M. W. Evans, On commutative p.p. rings, Pacific J. Math. 41(1972), 687-697.

A. Ghorbani and M. R. Vedadi, Epi-retractable modules and some applications,

Bull. Iran. Math. Soc. 35(1)(2009), 155-166.

K. R. Goodearl and A. K. Boyle, Dimension theory for nonsingular injective

modules, Memoirs Amer. Math. Soc. 7(177), 1976.

A. Hattori, A foundation of the torsion theory over general rings, Nagoya Math.

J. 17(1960), 147-158.

C. Y. Hong, N. K. Kim and T. K. Kwak, Ore extensions of Baer and p.p.-rings, J.

Pure Appl. Algebra 151(3)(2000), 215-226.

I. Kaplansky, Rings of operators, Math. Lecture Note Series, Benjamin, New York,

J. Krempa, Some examples of reduced rings, Algebra Colloq. 3(4)(1996), 289-300.

T. Y. Lam, Exercises in classical ring theory, Springer-Verlag, New York, 1995.

J. Lambek, On the representation of modules by sheaves of factor modules, Canad.

Math. Bull. 14 (3)(1971), 359-368.

T. K. Lee and Y. Zhou, Reduced modules, Rings, modules, algebras and abelian

groups, 365-377, Lecture Notes in Pure and Appl. Math., 236, Dekker, New York,

(2004).

B. L. Osofsky, A counter-example to a lemma of Skornjakov, Pacific J. Math.

(1965), 985-987.

R. Raphael, Some remarks on regular and strongly regular rings, Canad. Math.

Bull. 17(5)(1974/75), 709-712.

S. T. Rizvi and C. S. Roman, Baer and quasi-Baer modules, Comm. Algebra

(2004), 103-123.

S. T. Rizvi and C. S. Roman, On direct sums of Baer modules, J. Algebra 321(2009),

-696.

J. E. Roos, Sur les categories spectrales localement distributives, C. R. Acad. Sci.

Paris 265(1967), 14-17.

B. Ungor, N. Agayev, S. Halicioglu and A. Harmanci, On principally quasi-Baer

modules, Albanian J. Math. 5(3)(2011), 165-173.

J. M. Zelmanowitz, Regular modules, Trans. Amer. Math. Soc. 163(1972), 341-355.


Refbacks

  • There are currently no refbacks.