Math @ Duke

Publications [#243901] of Ezra Miller
Papers Accepted
 with Kahle, T; Miller, E, Decompositions of commutative monoid congruences and binomial ideals,
Algebra & Number Theory, vol. 8 no. 6
(2012),
pp. 12971364 (62 pages.) [math.AC/1107.4699], [doi]
(last updated on 2018/10/21)
Abstract: We demonstrate how primary decomposition of
commutative monoid congruences fails to
capture the essence of primary
decomposition in commutative rings by
exhibiting a more sensitive theory of
mesoprimary decomposition of
congruences, complete with witnesses,
associated prime objects, and an analogue
of irreducible decomposition called
coprincipal decomposition. We lift
the combinatorial theory of mesoprimary
decomposition to arbitrary binomial ideals in
monoid algebras. The resulting binomial
mesoprimary decomposition is a new type
of intersection decomposition for binomial
ideals that enjoys computational efficiency
and independence from ground field
hypotheses. Furthermore, binomial primary
decomposition is easily recovered from
mesoprimary decomposition, as is binomial
irreducible decomposition  which was
previously not known to exist  from
binomial coprincipal decomposition.


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