27 research outputs found
A characterization of some families of Cohen--Macaulay, Gorenstein and/or Buchsbaum rings
We provide algorithmic methods to check the Cohen--Macaulayness,
Buchsbaumness and/or Gorensteiness of some families of semigroup rings that are
constructed from the dilation of bounded convex polyhedrons of .
Some families of semigroup rings are given satifying these properties
Analog front-end ASIC requirements for a FDM broadband powerline system enabling co-existence
Factorization invariants in numerical monoids
Nonunique factorization in commutative monoids is often studied using
factorization invariants, which assign to each monoid element a quantity
determined by the factorization structure. For numerical monoids (co-finite,
additive submonoids of the natural numbers), several factorization invariants
have received much attention in the recent literature. In this survey article,
we give an overview of the length set, elasticity, delta set,
-primality, and catenary degree invariants in the setting of numerical
monoids. For each invariant, we present current major results in the literature
and identify the primary open questions that remain