Sentence examples for flat dimension from inspiring English sources
A random shoe separated from its owner still held a constellation of foot bones that had collapsed to one flat dimension without the flesh that once gave them shape.
Consequently, the flat dimension of a Leavitt path algebra L K ( E ) equals 1 precisely when L K ( E ) is not von Neumann regular (i.e., when there are L K ( E ) -modules which are not flat).
So the flat dimension, and therefore also the global dimension, of L K ( 1, 2 ) ⊗ K L K ( 1, 2 ) is at least 2, so that L K ( 1, 2 ) ⊗ L K ( 1, 2 ) cannot be a Leavitt path algebra (again using Theorem 6 ′ ), and so can't be isomorphic to L K ( 1, 2 ).
The first proof (unpublished), offered by Warren Dicks, utilized a classical result of Cartan and Eilenberg [53, Theorem X1.3.1], which yields that the flat dimension of a tensor product is at least the sum of the flat dimensions of the two algebras.
□ For formal algebras concentrated in degree zero, the above corollary is the elementary fact that flat dimension is less than or equal to projective dimension.
The disc's flat dimensions offered a more convenient means of storing many songs than the three-dimensional Edison cylinder.
But in trapping Ms. Reza's play in the framed, flat dimensions of the screen, the director destroys it.
Where Joan Miro espoused the "automatic" approach, letting the unconscious determine the line, and Dali reached into the dreamworld, returning to three-dimensional and figurative art in his later work, Magritte kept rigidly to his canon of flat dimensions and frozen images.
"When you look any animals around here--lions, zebras, elephants," Cynthia offers, "you're seeing just two flat dimensions.
We show that the weak (i.e., flat) homological dimension of O(Y) as a Fréchet O X -module equals the cO X -moduleof Y in X.
The notion of contemporaneity itself, precisely because it seems to crush time into a flat, simultaneous dimension, is no longer sufficient to express this mixing, intersecting and diversifying of time that is modelling the territory (Didi-Huberman [2000]; Agamben [2008]).
