Abstract:
The paper continues prevoius author publications on a constructive mathematics approach in computational algebra using a language with dependent types.
A constructive expression for the notion of a domain with factorization
to primes for a monoid and for a ring
possessing certain additionnal properties is obtained.
A way to achieve constructed machine-checked proofs
for theorems that relate the factorization notion
for domains of different kinds is discussed.
All the described methods and proofs are completely implemented as a working program written in the Agda functional language.
(In Russian).
Key words and phrases:constructive mathematics, computer algebra, dependent types, functional programming, Agda.