Meanings
- uncountablealgebraA relatively new discipline in mathematics that combines techniques and concepts from combinatorics and commutative algebra, and in which the geometry of convex polytopes also plays a significant role.
This construction has become a fundamental tool in combinatorial commutative algebra due to the work of Stanley, Hochster and Reisner ([Ho77], [S75], [S96], [R76]).
2011, Viviana Ene, Jũrgen Herzog, Gröbner Bases in Commutative Algebra, American Mathematical Society, page 882 more examples
2013, Anna M. Bigatti, Philippe Gimenez, Eduardo Sáenz-de-Cabezón Introduction, Anna M. Bigatti, Philippe Gimenez, Eduardo Sáenz-de-Cabezón (editors), Monomial Ideals, Computations and Applications, Springer, page vii, Monomial ideals and algebras are among the simplest structures in commutative algebra and the main objects in combinatorial commutative algebra.
Using techniques from combinatorial commutative algebra [MS05, KM], they showed that certain lattice games admit a particular type of algebraic decomposition known as affine stratifications, from which a finitely representable winning strategy can be recovered.
2013, Aaron N. Siegel, Combinatorial Game Theory, American Mathematical Society, page 269
Translations
Polish kombinatoryczna algebra przemienna
- kombinatoryczna algebra przemiennadiscipline in mathematics
Cite this entry
combinatorial commutative algebra. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/combinatorial%20commutative%20algebra
“combinatorial commutative algebra.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/combinatorial%20commutative%20algebra. Accessed November 4, 2026.
WatkinsX Dictionary, s.v. “combinatorial commutative algebra,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/combinatorial%20commutative%20algebra.
Source: combinatorial commutative algebra on Wiktionary, CC BY-SA 4.0.