Weakly Unique Factorization Modules

https://doi.org/10.22146/jmt.64981

I Putu Yudi Prabhadika(1*), Sri Wahyuni(2)

(1) Gadjah Mada University
(2) Gadjah Mada University
(*) Corresponding Author

Abstract


Let D be an integral domain. An element a in D is said to have a factorization
if a = p_1p_2 . . . p_n with p_1, p_2, ..., p_n is an irreducible element in D. Futhermore, given the defnition of unique factorization domain that is an integral domain with each nonzero nonunit elements in it has an unique factorization. Based on the fact that ring and modules have many interrelated properties, motivate the idea about denition of unique factorization modules and weakly unique factorization modules. It will be shown the properties and characterization of weakly unique factorization modules. Futhermore, will be shown the correlation between weakly unique factorization modules and unique factorization modules.


Keywords


irreducible elements; ring; modules; factorization; unique factorization modules.

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References

Adkins, W.A., Weintraub, S.H., Algebra: An Approach via Module Theory, Springer-Verlag, New York, 1992.

Lu, C. P., Factorial Modules, Rocky Mountain Journal of Mathematics, Vol. 7 No. 1 (1977), pp. 125-139.

Malik, D. S., Mordeson, J.M., Sen, M.K., Fundamentals of Abstract Algebra, McGraw-Hill Companies, Inc., Singapore, 1997.

Nicolas, A., Modules Factoriels, Seminaire Dubrell-Pisot, Vol. 20 No. 10 (1967), pp. 1-12.

Oral, K.H., Tekir, U., Agargun, A.G., Weakly Unique Factorization Modules, Tamkang Journal of Mathematics, Vol. 41 No. 3 (2016), hal. 245-252.

Wahyuni, S., Wijayanti, I.E., Yuwaningsih, D.A., Hartanto, A.D., Teori Ring dan Modul, Gadjah Mada University Press, 2016.



DOI: https://doi.org/10.22146/jmt.64981

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