Sentence examples for primary decomposition over from inspiring English sources

Mesoprimary decompositions are highly combinatorial in nature, and are designed to parallel standard primary decomposition over Noetherean rings.

In this paper, we generalize mesoprimary decomposition from binomial ideals to "binomial submodules" of certain graded modules over a monoid algebra, analogous to the way primary decomposition of ideals over a Noetherean ring R generalizes to R-modules.

The algorithm uses primary decomposition of monomial ideals as the principal tool.

The model simulates the primary decomposition process well with the calculated rate constants.

Rings having the primary decomposition property are called "Laskerian rings" in his honor.

In his 1905 article on commutative algebra, Lasker introduced the theory of primary decomposition of ideals, which has influence in the theory of Noetherian rings.

Lasker was also a research mathematician who was known for his contributions to commutative algebra, which included proving the primary decomposition of the ideals of polynomial rings.

Recent results of Kahle and Miller give a method of constructing primary decompositions of binomial ideals by first constructing "mesoprimary decompositions" determined by their underlying monoid congruences.

"The primary's over," Mario Cuomo told writer.

In fact, the Department of Energy and its laboratories have never found any such decomposition over the past 30 years of rigorous studies.

The RF + CR treatment had the highest decomposition rate constant value (0.098 week−1) indicating fast decomposition over all treatments.