Using Divisor Function and Euler Product Function in Abstract Algebra Concepts
K. Subbanna,
S. Venkatarami Reddy,
S. Gouse Mohiddin,
R. Bhuvana Vijaya
Issue:
Volume 5, Issue 4, August 2019
Pages:
57-62
Received:
10 August 2019
Accepted:
19 September 2019
Published:
9 October 2019
Abstract: Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties, such as whether a ring admits unique factorization, the behavior of ideals, and the Galois groups of fields, can resolve questions of primary importance in number theory. In this paper for the most part centered around number theory ideas which are utilized in different themes like group theory and ring theory, these speculations are extremely unique ideas to comprehend among this we might want to express our perspectives as far as number hypothesis/theory ideas, such as, to calculate some subgroups of a cyclic group, number of ideals, principal ideals of a ring and number of generators of a cyclic group as far as both regular procedure and number speculation/hypothesis thoughts.
Abstract: Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. Th...
Show More
Some Property of Finite Sum of Weighted Composition and Weighted Frobenius-Perron Operators
Issue:
Volume 5, Issue 4, August 2019
Pages:
63-67
Received:
26 May 2019
Accepted:
1 July 2019
Published:
25 October 2019
Abstract: The study of finite sum of weighted composition operators on Lp - spaces has received considerable attention in 2012. Characterizations, basic properties of this operators have been obtained. Weighted composition operators are a general class of operators and they appear naturally in the study of surjective isometries on most of the function spaces, semi grup theory, dynamic systems etc. This type of operators are a generalization of multiplication operators and composition operators. In this paper the relations among completely continuous and M - weakly compact of finite sum of weighted composition operators between Lp(μ) - spaces described, we also obtain some necessary and sufficient conditions for Fredholmness of the finite sum of weighted composition operators.
Abstract: The study of finite sum of weighted composition operators on Lp - spaces has received considerable attention in 2012. Characterizations, basic properties of this operators have been obtained. Weighted composition operators are a general class of operators and they appear naturally in the study of surjective isometries on most of the function spaces...
Show More
