Strong Gröbner bases for polynomials over a principal ideal ring

DOI10.1017/S0004972700019973zbMath1046.13019MaRDI QIDQ2777726

Ana Sălăgean, Graham H. Norton

Publication date: 2001

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

algorithmsprincipal ideal domainrings with zero-divisorsstrong Gröbner bases

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Principal ideal rings (13F10)

Related Items (15)

A Gröbner basis algorithm for ideals over zero-dimensional valuation rings ⋮ Dynamical Gröbner bases ⋮ On cyclic codes over Galois rings ⋮ Finite multidimensional behaviors ⋮ 1-generator quasi-cyclic codes over finite chain rings ⋮ GVW algorithm over principal ideal domains ⋮ Efficient Gröbner bases computation over principal ideal rings ⋮ Repeated-root cyclic and negacyclic codes over a finite chain ring ⋮ Buchberger-Zacharias theory of multivariate Ore extensions ⋮ Cyclic Codes over Galois Rings ⋮ Relative Gröbner and involutive bases for ideals in quotient rings ⋮ On the structure of 1-generator quasi-polycyclic codes over finite chain rings ⋮ APPLYING BUCHBERGER'S CRITERIA FOR COMPUTING GRÖBNER BASES OVER FINITE-CHAIN RINGS ⋮ On \(\mathbb{Z}_2\mathbb{Z}_4\)-additive polycyclic codes and their Gray images ⋮ Cyclic codes and minimal strong Gröbner bases over a principal ideal ring.

Uses Software

• FGb
• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• The Magma algebra system. I: The user language
• On the structure of linear and cyclic codes over a finite chain ring
• Modular and \(p\)-adic cyclic codes

This page was built for publication: Strong Gröbner bases for polynomials over a principal ideal ring