Finite-direct-injective modules

Yıl 2018, , 143 - 152, 11.01.2018

Sanjeev Kumar Maurya Ashok Ji Gupta

https://doi.org/10.24330/ieja.373656

Cited By: 2

Öz

In this paper, we generalize the concept of direct-injective modules

to finite-direct-injective modules. Various basic properties of these modules are

studied. We show that the class of finite-direct-injective modules lies between

the class of direct-injective modules and the class of simple-direct-injective

modules. Also, we characterize semisimple artinian rings, V -rings and regular

rings in terms of finite-direct-injective modules.

Anahtar Kelimeler

C2-module, C3-module, nite-direct-injective module, regular ring

Kaynakça

• M. Alkan and A. Harmanci, On summand sum and summand intersection property of modules, Turkish J. Math., 26(2) (2002), 131-147.
• V. Camillo, Y. Ibrahim, M. Yousif and Y. Zhou, Simple-direct-injective mod- ules, J. Algebra, 420 (2014), 39-53.
• H. Q. Dinh, A note on pseudo-injective modules, Comm. Algebra, 33(2) (2005), 361-369.
• N. Er, S. Singh and A. K. Srivastava, Rings and modules which are stable under automorphisms of their injective hulls, J. Algebra, 379 (2013), 223-229.
• J. L. Garcia, Properties of direct summands of modules, Comm. Algebra, 17(1) (1989), 73-92.
• A. W. Goldie, Torsion-free modules and rings, J. Algebra, 1 (1964), 268-287.
• G. Lee, S. T. Rizvi and C. S. Roman, Dual Rickart modules, Comm. Algebra, 39(11) (2011), 4036-4058.
• T. K. Lee and Y. Zhou, Modules which are invariant under automorphisms of their injective hulls, J. Algebra Appl., 12(2) (2013), 1250159 (9 pp).
• S. H. Mohamed and B. J. Muller, Continuous and Discrete Modules, London Mathematical Society Lecture Note Series, 147, Cambridge University Press, Cambridge, 1990.
• W. K. Nicholson, Semiregular modules and rings, Canad. J. Math., 28(5) (1976), 1105-1120.
• W. K. Nicholson and Y. Zhou, Semiregular morphisms, Comm. Algebra, 34(1) (2006), 219-233.
• B. L. Osofsky, Rings all of whose nitely generated modules are injective, Paci c J. Math., 14 (1964), 645-650.
• B. L. Osofsky and P. F. Smith, Cyclic modules whose quotients have all com- plement submodules direct summands, J. Algebra, 139(2) (1991), 342-354.
• V. S. Ramamurthi and K. M. Rangaswamy, On nitely injective modules, J. Austral. Math. Soc., 16 (1973), 239-248.
• Y. Utumi, On continuous rings and self injective rings, Trans. Amer. Math. Soc., 118 (1965), 158-173.
• R. Wisbauer, Foundations of Module and Ring Theory, Algebra, Logic and Applications, 3, Gordon and Breach Science Publishers, Philadelphia, PA, 1991.