Abstract
In the author’s previous papers, the connection between generating syzygy modules by binary relations, the property of a commutative ring to be arithmetical (that is to have a distributive ideal lattice), and the use of the so-called S-polynomials in the standard basis theory were discussed. In this note, these connections are considered in a more general context. As an illustration of the usefulness of these considerations, a simple proof of some well-known fact from commutative algebra is given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. S. Golod, “Standard bases and homology,” in: L. L. Avramov and K. B. Tchakerian, eds., Algebra: Some Current Trends. Proc. of the 5th National School in Algebra held in Varna, Bulgaria, Sept. 24 – Oct. 4, 1986, Lect. Notes Math., Vol. 1352, Springer (1988), pp. 105–110.
E. S. Golod, “On noncommutative Gr¨obner bases over rings,” Fundam. Prikl. Mat., 10, No. 4, 91–96 (2004).
E. S. Golod, “Arithmetical rings, endomorphisms, and Gr¨obner bases,” Usp. Mat. Nauk, 60, No. 1, 167–168 (2005).
C. Huneke, “On the symmetric and Rees algebra of an ideal generated by a d-sequence,” J. Algebra, 62, No. 2, 268–275 (1980).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 3, pp. 127–134, 2010.
Rights and permissions
About this article
Cite this article
Golod, E.S. Distributivity, binary relations, and standard bases. J Math Sci 177, 862–867 (2011). https://doi.org/10.1007/s10958-011-0514-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-011-0514-4