Dynamical ideals of non-commutative rings

TL;DR

This paper introduces a dynamical analog of prime ideals in simple non-commutative rings, providing a factorization theorem and applying it to classify surface knots and links in 4-manifolds.

Contribution

It develops a new dynamical framework for prime ideals in non-commutative rings and applies it to topological classification problems.

Findings

Established a factorization theorem for dynamical ideals.

Classified surface knots and links in 4-dimensional manifolds.

Introduced a novel dynamical approach to non-commutative algebra.

Abstract

A dynamical analog of the prime ideals for simple non-commutative rings is introduced. We prove a factorization theorem for the dynamical ideals. The result is used to classify the surface knots and links in the smooth 4-dimensional manifolds.