Work

Permanental ideals of symmetric matrices

Year: 2025

Type: article

Abstract: In this article, we study the ideal generated by 2 × 2 2\times 2 permanents of a symmetric matrix. We denote this ideal by P 2 ( X ) P_2(X) where X X is a symmetric matrix. We compute a Gröbner basis, dimension, depth, minimal primes, and a primary decomposition of P 2 ( X ) P_2(X) . It can be seen that the answer is reliant on whether the characteristic of the base field is two, and thus these ideals constitute a class of ideals whose algebraic properties depend on characteristics of the base field.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17512

Author: Trung Chau

Institution: Chennai Mathematical Institute

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Purdue University, Infosys Foundation