An Introduction To The Symbolic Turiyam R-Modules and Turiyam Modulo Integers

Abstract

Recently, Turiyam set is introduced for dealing the fourth dimensional data sets. These types of data sets exists when an expert unable to categorize them in Euclidean, Non-Euclidean, Hybrid or NeutroGeometry. To deal with these types of data set Turiyam matrix and its algebra is required. Hence the current paper introduce the concept of Symbolic Turiyam R-module as a generalization of the corresponding neutrosophic one by using the algebra of symbolic Turiyam set. The paper also presents concept pf finite Turiyam modulo integer and illustrate many examples to show and clarify the validity of this work.

Hibrid Δ‐Statistical Convergence for Neutrosophic Normed Space

“…e concept of Turiyam feature, first defined by Singh, was examined in [30] with the structure of Turiyam R-Modules and Turiyam modulo integers. Since it is considered that the 4th component, which is described as the Turiyam feature, is included in the 3rd component where the uncertainty situations are given, the study was built with 3 components.…”

Conjectures for Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic Refined Integers

“…Recently, symbolic Turiyam rings [16] its modules [17] and matrix [18] is studied for dealing the data with Turiyam set [19]. In this section, the invertibility of a symbolic Turiyam integer is discussed as follows:…”

“…In the theory of rings, it was very useful to build a bigger ring contains another one, which it is called a ring extension [1][2][11][12][13][14][15]. Recently, it is studied for dealing the four way data analysis using Turiyam ring [16] and its extensive properties [17][18][19] for solving various decision making problems. However basic proof of some conjecture and equations are required to understand the usability of mathematical algebra [20].…”

“…For more information about neutrosophic algebra [5][6][7][8][9][10] or four way Turiyam ring author can refer to [16][17][18][19] for basic understanding of mathematical proof [20].…”

Invers Moore-Penrose pada Matriks Turiyam Simbolik Real

“…Pengembangan konsep dan penerapan matriks turiyam simbolik ini baru dibahas oleh beberapa peneliti, dalam ilmu matematika konsep Turiyam yang telah dibahas yaitu, terkait pengantar Turiyam simbolik grup dan substruktur AH [13], pengantar konsep matriks Turiyam simbolik [14], pengantar ruang vektor dan bilangan kompleks Turiyam simbolik [15], representasi data dimensi keempat dan analisisnya menggunakan konteks Turiyam [9], pengantar Turiyam simbolik R-modulo dan modulo bilangan bulat Turiyam simbolik [14], Turiyam simbolik ring [10], Turiyam simbolik grup [13], representasi data dimensi keempat himpunan Turiyam [6], dan data dengan himpunan Turiyam untuk pengolahan informasi kuantum dimensi keempat [16]. Begitu juga penelitian mengenai invers Moore-Penrose telah dilakukan oleh beberapa peneliti yaitu, invers Moore-Penrose pada free matrix [4], invers Moore-Penrose sebagai invers matriks [17], invers Moore-Penrose pada matriks kompleks, invers Moore-Penrose pada matriks atas aljabar Max-Plus tersimetri [12], dan perhitungan cepat matriks invers Moore-Penrose [18].…”