Papers by Bhavanari Satyanarayana
International Journal of Statistics and Applied Mathematics
Indian mathematics has its deep roots in the Vedas, different from what is known as Vedic Mathema... more Indian mathematics has its deep roots in the Vedas, different from what is known as Vedic Mathematics. Vedic age gave rise to a new era of progress in the field of Science, Technology and Development. The Hindu Scripture Vedas is synonymous with all kinds of original source of knowledge and intellectual wisdom in the universe leading to modern knowlege in modern mathematics. Indian mathematicians made tremendous contributions to the entire world of Mathematics and Science. Decimal number system as well as the invention of zero (0) are among the greatest contributions of Indian mathematicians. The theory of trigonometry, Mathematical Modelling, Algebra, algorithm, modern arithmetic, sine and cosine functions leading to modern trigonometry, Diophantine equation, square root, cube root, negative numbers are also developed by Indian mathematicians. In this review article, the work of some of the renowned Indian mathematicians from Indus Valley civilization and the Vedas to modern times are covered in short with the hope that it may reveal hidden fundamental mathematical ideas as basic ideal tools which may usefully motivate for further research work in every domain of mathematical sciences, natural and applied sciences, engineering and social sciences. Moreover, there are many more remarkable Indian mathematicians who contributed to the origin of mathematical sciences. They have made several general contributions to mathematics that have significantly influenced scientists and mathematicians in the modern times.
Mathematical Foundation of Computer Science, 2019
The main purpose of this paper is to investigate ordered -semihypergroups in the general terms o... more The main purpose of this paper is to investigate ordered -semihypergroups in the general terms of ordered -hyperideals. We intro-duce ordered (generalized) (m; n)--hyperideals in ordered -semihypergroups. Then, we characterize ordered -semihypergroup by ordered (generalized) (0; 2)- -hyperideals, ordered (generalized) (1; 2)-{hyperideals and ordered (general- ized) 0-minimal (0; 2)--hyperideals. Furthermore, we investigate the notion of ordered (generalized) (0; 2)-bi--hyperideals, ordered 0-(0; 2) bisimple ordered -semihypergroups and ordered 0-minimal (generalized) (0; 2)-bi--hyperideals in ordered -semihyperoups. It is proved that an ordered -semihypergroup S with a zero 0 is 0-(0; 2)-bisimple if and only if it is left 0-simple.
International Educational Scientific Research Journal, 2016
In this paper we consider the ringR of 2X2 - matrices over Z2 (the ring of integers modulo 2). W... more In this paper we consider the ringR of 2X2 - matrices over Z2 (the ring of integers modulo 2). We constructed ZDG(R) (the zero divisor graph of the ring R) and obtained a simple fundamental important result on ZDG(R). Finally we observed some basic properties of ZDG(R).
Mathematical Foundation of Computer Science, 2019
Mathematical Foundation of Computer Science, 2019
Mathematical Foundation of Computer Science, 2019
The algebraic system ‘Gamma near-ring’, a generalization of both the algebraic structures ‘gamma ... more The algebraic system ‘Gamma near-ring’, a generalization of both the algebraic structures ‘gamma ring’ and ‘near-ring’, was introduced by Satyanarayana [8]. Later several authors were studied the system gamma near-ring. In this paper, we define ‘abstract affine gamma near-ring M’ and finally, obtain an equivalent condition for a subgroup of (M, +) to be a quasi-ideal of M in a class of abstract affine gamma near-rings.
GIS SCIENCE JOURNAL, 9(8)(2022), 370-375. Dr. Abul Basar, Dr. Ayaz Ahmad, Dr Poonam Kumar Sharma and Professor Bhavanari Satyanarayana, 2022, 2022
In this paper, we introduce relative hyperideals, relative quasi-hyperideals, relative bi-hyperid... more In this paper, we introduce relative hyperideals, relative quasi-hyperideals, relative bi-hyperideals, relative prime hyperideal, relative semiprime hyperideal, relative quasi-prime hyperideal, relative quasi-semiprime hyperideal, relative quasi-irreducible hyperideal, and relative regularity in ordered LA-semihypergroups. The results in this paper cleanly generalize those in LA-semigroups, LA-Γ-semigroups, ordered LA-semigroups, ordered LA-Γ-semigroups, LA-semihypergroups, LA-Γ-semihypergroups, ordered LA-Γsemihypergroups as well as in ordered LA-semihypergroups by these novel relative hyperideals.
GIS SCIENCE JOURNAL, 9(7)(2022), 2793-2803. Dr. Abul Basar, Dr. Ayaz Ahmad, Dr Poonam Kumar Sharma and Professor Bhavanari Satyanarayana, 2022
In this paper, we introduce some mathematical objects, viz., relative ordered prime, relative ord... more In this paper, we introduce some mathematical objects, viz., relative ordered prime, relative ordered completely prime, relative ordered semiprime, and relative ordered completely semiprime right Γ-hyperideals in ordered Γ-semihypergroups. We also introduce the concepts of relative ordered prime right associated Γ-hyperideals. Moreover, we characterize ordered Γ-semihypergroups by relative ordered prime, relative ordered completely prime, relative ordered semiprime, and relative ordered completely semiprime right Γ-hyperideals.
European Journal of Mathematics and Applications, 2022
In this paper, we introduce G-hyperideal, G-prime hyperideal, G-prime-bihyperideal, and G-weakly ... more In this paper, we introduce G-hyperideal, G-prime hyperideal, G-prime-bihyperideal, and G-weakly prime hyperideal in ordered semihypergroups and we also define G-regular ordered hypersemigroups as well as G-semisimple ordered hypersemigroups. Thereby, we extend the results to the broader and abstract setting of ordered hypersemigroups, this also strengthens previous generalizations relating to rings, semigroups and other algebraic structures.
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1988
Introduction. Let R be a fixed (not necessarily commutative) ring with. unity. Throughout this pa... more Introduction. Let R be a fixed (not necessarily commutative) ring with. unity. Throughout this paper we are concerned with left R-modules and M stands for a unitary R-module. The submodule generated by an element a e M is denoted by Ra. Like in Fleury [1], Goldie [2], Reddy and Satyanarayana [3], Satyanarayana [4] and Sharpe and Vamoes [5] we shall use the following terminology. A non-zero submodule K of M is called essential in M (or M is an essential extension of K) if K A-0 for any other submodule A of M, implies A-0. M has finite Goldie dimension (abbr. FGD) if M does not contain a direct sum of infinite number of non-zero submodules. Equivalently, M has FGD if for any strictly increasing sequence H0, H, of submodules of M, there is an integer i such that for every />i, H is an essential submodule in H+. M is uniform if every
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1983
Introduction. Throughout the paper, M stands for a F-ring, as defined by Barnes [1]. We shall uti... more Introduction. Throughout the paper, M stands for a F-ring, as defined by Barnes [1]. We shall utilize the standard notations and definitions in Barnes [1] and Hsu [2]. In [2] Hsu has introduced the
Proceedings of Indian National Science Academy, 2015
ON FINITE SPANNING DIMENSION IN N-GROUPS
Preliminary definitions. If a is an element of the F-ring M, then (a) denotes the principal ideal... more Preliminary definitions. If a is an element of the F-ring M, then (a) denotes the principal ideal generated by a. If S is a subset of M, we call S an sp-system if S=i or a eS implies (a)S=. A nonempty subset S ofM is called a g-sp-system if S contains an sp-system .S’ such that g(x) S’=O for every element x of S, where S’ is called a kernel of S. An ideal I ofM is said to be g-halfprime if C(I)=M\I is a g-sp-system. Example. Consider Z, the ring of integers, as a F-ring with F =Z. Let p, q be two distinct prime numbers. Define g(a)-({a, pq}). Now g(pq)=(pq) and hence C((pq)) is g-sp-system with kernel C((pq)), which is not a g-system.
Uploads
Papers by Bhavanari Satyanarayana