On the Structure of a Class of Galois Ring Module Idealization | Chapter 7 | Mathematics and Computer Science: Contemporary Developments Vol. 7

Let R_o be a Galois ring and U is a finitely generated R_o- module. Consider an idealization of U expressed as R = R_o \(\bigoplus\) U endowed with a suitable multiplication. We explore the structure of R through its group of units R^x and the graph of its zero divisors \(\Gamma\)(R). The study involves an investigation on the overarching interplay between the ring theoretical properties of R, the group theoretic properties of R^x and the graph theoretic properties of \(\Gamma\)(R). Since R is a finite ring with identity, the convention that each element of R is either a unit or a zero divisor has been extensively used to drive the concept of classification of the elements of R. The units of R have been classified, the automorphisms of R have been determined and the zero divisors of R have been characterized.

 

Author (s) Details

Owino Maurice Oduor
Department of Mathematics, Actuarial and Physical Sciences, University of Kabianga, P.O Box 2030-20200, Kericho, Kenya.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v7/2728

Two Different Improved Bounds of Rivlin's Type Inequality on Polynomial Diversified under the Same Hypotheses| Chapter 5 | Research Highlights in Mathematics and Computer Science Vol. 5

Let p(z) be a complex polynomial of quality n. The problem of best closeness under different restrictions on the zeros had existed attracting many, containing renowned scientists and mathematicians like Mandeleev, Markov twins and Bernstein. Their works had existed studied extensively by many mathematicians that resulted in rich accumulation of inequalities concerning complex polynomials. In this item, we discuss in a concise manner two different improved bounds of Rivlin's type prejudice on polynomial diversified under the unchanging hypotheses.

Author(s) Details:

Barchand Chanam,
Department of Mathematics, National Institute of Technology Manipur, Langol 795004, India.

Please see the link here: https://stm.bookpi.org/RHMCS-V5/article/view/9380