Algunos aspectos de la teoría de casi-anillos de polinomios
- Gutiérrez Gutiérrez, Jaime
Defence university: Universidad de Cantabria
Year of defence: 1988
- Tomás Jesús Recio Muñiz Chair
- Juan Manuel de Olazábal Malo de Molina Secretary
- Günter F. Pilz Committee member
- Miguel Torres Iglesias Committee member
- Juan Gabriel Tena Ayuso Committee member
Type: Thesis
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.