Formalizing Ring Theory in PVS (short paper)

Authors: Andréia B. Avelar, Thaynara A. de Lima and André Luiz Galdino

Paper Information

Title:Formalizing Ring Theory in PVS (short paper)
Authors:Andréia B. Avelar, Thaynara A. de Lima and André Luiz Galdino
Proceedings:ITP Papers
Editors: Jeremy Avigad and Assia Mahboubi
Keywords:PVS, Formal proofs, Ring Theory

ABSTRACT. This work presents the ongoing specification and formalization in the PVS proof assistant of some definitions and theorems of ring theory in abstract algebra, and briefly presents some of the results intended to be formalized. So far, some important theorems from ring theory were specified and formally proved, like the First Isomorphism Theorem, the Binomial Theorem and the lemma establishing that every finite integral domain with cardinality greater than one is a field. The goal of the project in progress is to specify and formalize in PVS the main theorems from ring theory presented in undergraduate textbooks of abstract algebra, but in the short term the authors intended to formalize: (i) the Second and the Third Isomorphism Theorems for rings; (ii) the primality of the characteristic of a ring without zero divisors; (iii) definitions of prime and maximal ideals and theorems related with those concepts. The developed formalization applies mainly a part of the NASA PVS library for abstract algebra specified in the theory algebra.

Talk:Jul 11 17:00 (Session 67C)