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Intan Muchtadi Alamsyah
Algebra Research Group Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung,
Mathematics

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Basis Normal Self-Dual dan Variannya Irwansyah Irwansyah; Ahmad Muchlis; Intan Muchtadi Detiena
Jurnal Matematika & Sains Vol 17, No 3 (2012)
Publisher : Institut Teknologi Bandung

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Abstract

Basis normal self dual banyak digunakan dalam kriptografi. Dengan menggunakan basis tipe ini, dapat dikonstruksi aritmatika dengan kompleksitas rendah di lapangan hingga seperti perkalian dan perpangkatan. Tetapi, kelas basis ini hanya terdapat di lapangan hingga tertentu yaitu pada  dengan q ganjil atau dengan q genap dan . Untuk mengatasi  kekurangan ini, didefinisikan basis normal weakly self dual dan basis normal almost weakly self dual. Tulisan ini merupakan survei tentang hubungan antara basis normal self dual dan kedua variannya tersebut di lapangan hingga tertentu. Kata kunci: Lapangan hingga, Basis normal self dual, Basis normal weakly self dual, Basis normal almost weakly self dual.   Self-Dual Normal Basis and Their Variants Abstract Self dual normal basis has many applications in cryptography. We can construct arithmatic devices with relatively small complexity in finite fields using this type of  basis, such as multiplications and exponentials. Unfortunately, this type of basis exists in some particular finite fields only, i.e. in  with q is odd or even and . To avoid this limitation, two variants of self dual normal basis are introduced, i.e. weakly self dual normal basis and almost weakly self dual normal basis. In this paper, we survey connections among three type of normal basis above in particular finite fields. Keywords : Finite fields, Self dual normal basis, Weakly self dual normal basis, Almost weakly self dual normal basis.
Auslander Reiten Quiver of Nakayama Algebra Nn-2,n Faisal Faisal; Irawati Irawati; Intan Muchtadi Alamsyah
Jurnal Matematika & Sains Vol 18, No 1 (2013)
Publisher : Institut Teknologi Bandung

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For an algebraically closed field K, given a finite dimensional K-algebra A of  finite representation-type, we can store all the information of the module category mod A by its Auslander Reiten quiver of mod A. In this paper, we will determine the Auslander Reiten quiver of Nakayama algebra Nn-2,n  for every natural number n greater than or equal to 3, that is the  Nakayama algebra KQ/I where Q is a linear orientation cyclic quiver with  vertices and  denotes the ideal of the path algebra KQ generated by the paths of length of n – 1. Keywords: AR-quiver , Nakayama algebra, Quiver.   Quiver Auslander Reiten dari Aljabar Nakayama Nn-2,n AbstrakDiberikan K-aljabar A berdimensi hingga tipe representasi hingga dengan K suatu lapangan yang tertutup secara aljabar,  kita dapat menyimpan semua informasi dari kategori modul kanan mod A menggunakan Auslander Reiten quiver (AR-quiver) dari mod A. Dalam artikel ini, kita akan menentukan quiver Auslander Reiten dari aljabar Nakayama untuk setiap bilangan asli n lebih besar sama dengan 3. Aljabar Nn-2,n adalah aljabar Nakayama KQ/I dimana Q adalah quiver siklis berorientasi linier dengan  titik dan I adalah ideal dari aljabar lintasan KQ yang dibangun oleh lintasan panjang n – 1. Kata Kunci : AR-quiver, Aljabar Nakayama, Quiver.
CHARACTERIZATION OF NAKAYAMA $m$-CLUSTER TILTED ALGEBRAS OF TYPE $A_n$ Faisal, Faisal; Muchtadi-Alamsyah, Intan
Journal of the Indonesian Mathematical Society Volume 22 Number 2 (October 2016)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.22.2.213.93-130

Abstract

Abstract. For any natural natural number m, the m-cluster tilted algebras are generalization of cluster tilted algebras. These algebras are defined as the endomorphism of certain objects in m-cluster category called m-cluster tilting objects. Finding such objectin the m-cluster category has become a combinatorial problem. In this article we charac-terize Nakayama m-cluster tilted algebras of type An by geometric description given byBaur and Marsh.DOI : http://dx.doi.org/10.22342/jims.22.2.213.93-130
Co-Authors Ahmad Muchlis Faisal Faisal Faisal Faisal Irawati Irawati Irwansyah Irwansyah