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"Aljabar max-plus merupakan sebuah aljabar yang banyak diterapkan dalam berbagai bidang, terutama permasalahan optimisasi. Sebagaimana pada ruang Euclid, konsep geometri seperti semiruang dan hiperbidang juga dapat diterapkan pada aljabar max-plus. Terdapat beberapa perbedaan dari semiruang dan hiperbidang pada aljabar max-plus dengan semiruang dan hiperbidang pada ruang Euclid. Perbedaan ini muncul karena aljabar max-plus memiliki operasi yang berbeda. Pada skripsi ini, dipelajari aspek geometri dari aljabar max-plus terutama pada semiruang dan hiperbidang. Selanjutnya dipelajari pula keterkaitan di antara komplemen semiruang dan hiperbidang.

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The max-plus algebra is an algebra which is used in many subjects, especially optimization problem. Similar with the Euclid space, some geometrical concept such as semispaces and hyperplanes can be defined in max-plus algebra. There are some differences between semispaces and hyperplanes in max-plus algebra and semispaces and hyperplanes in the Euclid space. These differences occur because the max-plus algebra has different operations. In this undergraduate thesis, some characteristic of semispace and hyperplane will be studied. Furthermore, the relation between complement semispaces and hyperplanes will also be studied."

"This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter.This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra. "

"Modul adalah struktur aljabar yang didefinisikan atas suatu gelanggang, dilengkapi oleh dua operasi dengan syarat-syarat tertentu. Salah satu jenis modul yang dipelajari dalam kajian teori modul adalah modul Noetherian. Suatu - modul adalah modul Noetherian jika -modul memenuhi kondisi rantai naik (ascending chain condition) atas submodul dari , sedangkan suatu gelanggang dikatakan gelanggang Noetherian jika gelanggang tersebut memenuhi kondisi rantai naik (ascending chain condition) atas ideal dari . Dalam skripsi ini dibahas mengenai kriteria dari suatu modul agar menjadi modul Noetherian, kriteria dari gelanggang agar menjadi gelanggang Noetherian, dan kriteria dari gelanggang, sehingga gelanggang polinomial dan gelanggang hasil bagi menjadi gelanggang Noetherian.

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Module, together with two operations satisfying some conditions, is an algebraic structure defined over a ring. Noetherian module is one type of module which is studied in module theory. An -module is said to be Noetherian module if it satisfies an ascending chain condition on its submodules and any ring is a Noetherian ring if it satisfies ascending chain condition on ideals of . This skripsi discusses about some criterias for module to be considered as Noetherian module, criteria for any ring to be considered as Noetherian ring, and criteria for a ring so that the polynomial ring of and the quotient ring of , where is any ideals of , is Noetherian as well."