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Keywords:
retractable module; FI-mono-retractable module; compressible module; fully invariant submodule
Summary:
We introduce the notion of FI-mono-retractable modules which is a generalization of compressible modules. We investigate the properties of such modules. It is shown that the rings over which every cyclic module is FI-mono-retractable are simple Noetherian $V$-ring with zero socle or Artinian semisimple. The last section of the paper is devoted to the endomorphism rings of FI-retractable modules.
References:
[1] El-Bast Z. A., Smith P. F.: Multiplication modules. Comm. Algebra 16 (1988), no. 4, 755–779. DOI 10.1080/00927878808823601 | MR 0932633
[2] Dung N. V., Huynh D. V., Smith P. F., Wisbauer R.: Extending Modules. Pitman Research Notes in Mathematics Series, 313, Longman Scientific & Technical, Harlow; John Wiley & Sons, New York, 1994. MR 1312366 | Zbl 0841.16001
[3] Faith C.: Algebra: Rings, Modules and Categories. I. Die Grundlehren der mathematischen Wissenschaften, 190, Springer, New York, 1973. MR 0366960
[4] Goodearl K. R.: Ring Theory. Nonsingular Rings and Modules. Pure and Applied Mathematics, 33, Marcel Dekker, New York, 1976. MR 0429962 | Zbl 0336.16001
[5] Özcan A. Ç., Harmanci A., Smith P. F.: Duo modules. Glasg. Math. J. 48 (2006), no. 3, 533–545. DOI 10.1017/S0017089506003260 | MR 2271381
[6] Ramamurthi V. S., Rangaswamy K. M.: Generalized $V$-rings. Math. Scand. 31 (1972), 69–77. DOI 10.7146/math.scand.a-11412 | MR 0321974
[7] Smith P. F., Vedadi M. R.: Essentially compressible modules and rings. J. Algebra 304 (2006), no. 2, 812–831. DOI 10.1016/j.jalgebra.2005.08.018 | MR 2264280
[8] Wijayanti I. E.: Coprime Modules and Comodules. Ph.D. Dissertation, Heinrich–Heine–Universität, Düsseldorf, 2006.
[9] Wisbauer R.: Foundations of Module and Ring Theory. Algebra, Logic and Applications, 3, Gordon and Breach Science Publishers, Philadelphia, 1991. MR 1144522 | Zbl 0746.16001
[10] Wisbauer R.: Modules and Algebras: Bimodule Structure and Group Actions on Algebras. Pitman Monographs and Surveys in Pure and Applied Mathematics, 81, Longman, Harlow, 1996. MR 1396313
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