Authors: Andrzej Okninski
Comments: 4 Pages.
In the present work we make a small step towards inding explicit formula for polynomial roots. xplicit formulae for simple real roots, based on the Frobenius companion matrix, are derived. After some modifications the method can be used to compute multiple or complex roots.
Here for the first time we introduce the semi open square using modulo integers. This square under addition modulo ‘n’ is a group, and however under product ‘x’ this semi open square is only a semigroup as under ‘x’ the square has infinite number of zero divisors.
We define the new type of rings called pseudo rings.
Several open problems are suggested.
In this book the authors introduce the notion of finite complex modulo integer intervals. Finite complex modulo integers were introduced by the authors in 2011. Now, using this finite complex modulo integer intervals several algebraic structures are built. Open problems are suggested.