Algunos aspectos de la teoría de casi-anillos de polinomios

  1. Gutiérrez Gutiérrez, Jaime

Defence university: Universidad de Cantabria

Year of defence: 1988

Committee:
  1. Tomás Jesús Recio Muñiz Chair
  2. Juan Manuel de Olazábal Malo de Molina Secretary
  3. Günter F. Pilz Committee member
  4. Miguel Torres Iglesias Committee member
  5. Juan Gabriel Tena Ayuso Committee member

Type: Thesis

Teseo: 19101 DIALNET lock_openUCrea editor

Abstract

In this dissertation we study several aspects of near-rings. In the first chapter we give an explicit description of the distributive elements of the near-ring of polynomials R[x], over a commutative ring R a with identity. We also find the distributive elements in the near-ring of formal power series over a commutative rings with identity. In the second chapter, we search rings which are contained in R[x], we prove that if R is an integral domain, the set of distributive elements contains the subrings of the near-rings of polynomials. We also investigate ideals I of the near-ring such that the quotient is ring. In the next chapter we find all maximal ideals in Z[x] and maximal full ideals in the composition rings. The last section we provide the first polynomial time algorithm for decomposing polynomials into indecomposable ones.