SIFAT-SIFAT RING PRESIMPLIFIABEL DAN RING PRESIMPLIFIABEL LEMAH

Deby Anastasya

doi:10.22146/jmt.76174

SIFAT-SIFAT RING PRESIMPLIFIABEL DAN RING PRESIMPLIFIABEL LEMAH

https://doi.org/10.22146/jmt.76174

Deby Anastasya^(1*)

(1) Gadjah Mada University
(*) Corresponding Author

Abstract

Let $R$ be a commutative ring and let $a, b \in R$. Then $a$ and $b$ said to be associates if $a~|~b$ and $b~|~a$, so $a=rb$ and $b=sa$ for some $r,s \in R$. Associates generalized to a ring motivate the idea about definition of pr\'{e}simplifiable ring and weakly pr\'{e}simplifiable ring. First of all, we provide definitions of very strong associates, strong regular associates, very strongly associate ring, and strongly regular associate ring. Furthermore,it will be shown the properties between pr\'{e}simplifiable ring and weakly pr\'{e}simplifiable ring.

Keywords

Very strongly associate ring, Strongly reguler associate ring, Pr\'{e}simplifiable ring, Weakly pr\'{e}simplifiable ring.

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References

Anderson, D.D., Axtell, M., Forman, S.J., dan Stickles, J. 2004. When are Associates Unit Multiples?. Rocky Mountain J. Math., Vol. 34 No. 3, pp. 811-828.

Anderson, D.D. dan Chun, S. 2014. Associate Elements in Commutative Rings. Rocky Mountain J. Math., Vol. 44 No. 3.

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

Mooney, C.P. dan Wang, Y. 2018. On τ-U-irreducible elements in Strongly Associate Ring. The Minnesota Journal of Undergraduate Mathematics, Vol. 4.

DOI: https://doi.org/10.22146/jmt.76174