REGULARITAS DAN RELASI GREEN PADA SEMIGRUP TRANSFORMASI LINEAR PARSIAL INJEKTIF DENGAN RESTRIKSI RANGE

Ade Ima Afifa Himayati(1*)


(1) Universitas Muhammadiyah Kudus
(*) Corresponding Author

Abstract


Injective partial linear transformations in the vector space V and the function composition operations form semigroups called semigroups of injective partial linear transformations denoted by I (V). Suppose Z is a subspace in a vector space V, then the set of all members of I (V) whose function results are contained in Z to the function composition operation is also a semigroup denoted by I (V, Z) which is called a semigroup of injectable partial linear transformations with range restrictions. . In this article, we will examine how the characteristics of regular elements and the characteristics of two set members in I (V, Z) are related to Green using the literature study method. The results of the research in this article are the necessary and sufficient conditions needed so that any element is called a regular element and the characteristics of the two members of the set I (V, Z) are related.


Keywords


Regularity, Green relation, Semigroups, Linear Transformation, Injevtive, Restricted Range

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References


Chaiya, Y., Pookpienlert, C., & Sanwong, J. (2019). Semigroups of linear transformations with fixed subspaces: Green’s relations, ideals and finiteness conditions. Asian-European Journal of Mathematics, 12(4), 1–12. https://doi.org/10.1142/S1793557119500621

Clifford, A.H., dan Preston, G.B., 1961, The Algebraic Theory of Semigroups, American Mathematical Society, Providence.

Green, J. A. (1951). On the Structure of Semigroups. The Annals of Mathematics, 54(1), 163. https://doi.org/10.2307/1969317

Howie, J. M., 1995, Fundamental of Semigroups Theory, Oxford University Press, Inc., Newyork.

Sangkhanan, K., & Sanwong, J. (2012). PARTIAL ORDERS ON SEMIGROUPS OF PARTIAL TRANSFORMATIONS WITH RESTRICTED RANGE. 86, 100–118. https://doi.org/10.1017/S0004972712000020

Sangkhanan, K., & Sanwong, J. (2014). Green’s relations and partial orders on semigroups of partial linear transformations with restricted range. Thai Journal of Mathematics, 12(1), 81–93.

Sanwong, J., & Sommanee, W. (2008). Regularity and green’s relations on a semigroup of transformations with restricted range. International Journal of Mathematics and Mathematical Sciences, 2008. https://doi.org/10.1155/2008/794013

Sullivan, R. P. (2005). Partial orders on linear transformation semigroups. 413–437.


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DOI: https://doi.org/10.26714/jkpm.7.2.2020.73-80

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Jurnal Karya Pendidikan Matematika | P-ISSN: 2339-2444 E-ISSN: 2549-8401