111 citations · 388 across the 47 of their papers we have counts for
19 papers · 1 filter
Minimal resolutions of lattice ideals
Yupeng Li, Ezra Miller, Erika Ordog
A canonical minimal free resolution of an arbitrary co-artinian lattice ideal over the polynomial ring is constructed over any field whose characteristic is 0 or any but finitely m…
Global dimension of real-exponent polynomial rings
Nathan Geist, Ezra Miller
The ring R of real-exponent polynomials in n variables over any field has global dimension n+1 and flat dimension n. In particular, the residue field k = R/m of R modulo its maxima…
Primary decomposition over partially ordered groups
Ezra Miller
Over any partially ordered abelian group whose positive cone is closed in an appropriate sense and has finitely many faces, modules that satisfy a weak finiteness condition admit f…
Essential graded algebra over polynomial rings with real exponents
Ezra Miller
The geometric and algebraic theory of monomial ideals and multigraded modules is initiated over real-exponent polynomial rings and, more generally, monoid algebras for real polyhed…
Modules over posets: commutative and homological algebra
Ezra Miller
The commutative and homological algebra of modules over posets is developed, as closely parallel as possible to the algebra of finitely generated modules over noetherian commutativ…
Minimal resolutions of monomial ideals
John Eagon, Ezra Miller, Erika Ordog
An explicit combinatorial minimal free resolution of an arbitrary monomial ideal in a polynomial ring in variables over a field of characteristic is defined canonically…