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Peak reduction technique in commutative algebra

Vladimir Shpilrain·Jie-Tai Yu
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Abstract

The "peak reduction" method is a powerful combinatorial technique with applications in many different areas of mathematics as well as theoretical computer science. It was introduced by Whitehead, a famous topologist and group theorist, who used it to solve an important algorithmic problem concerning automorphisms of a free group. Since then, this method was used to solve numerous problems in group theory, topology, combinatorics, and probably in some other areas as well. In this paper, we give a survey of what seems to be the first applications of the peak reduction technique in commutative algebra and affine algebraic geometry.

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Vladimir Shpilrain, Jie-Tai Yu. 1999-12-20. Peak reduction technique in commutative algebra. https://arxiv.org/abs/math/9912156

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