73 citations · 140 across the 7 of their papers we have counts for
9 papers
Bi-atomic classes of positive semirings
Nicholas R. Baeth, Scott T. Chapman, Felix Gotti
Let be a nonnegative semiring of the real line, called here a positive semiring. We study factorizations in both the additive monoid and the multiplicative monoid $(S\s…
Lattices over Bass rings and graph agglomerations
Nicholas R. Baeth, Daniel Smertnig
We study direct-sum decompositions of torsion-free, finitely generated modules over a (commutative) Bass ring through the factorization theory of the corresponding monoid $T(R)…
Factorizations in upper triangular matrices over information semialgebras
Nicholas R. Baeth, Felix Gotti
An integral domain (or a commutative cancellative monoid) is atomic if every nonzero nonunit element is the product of irreducibles, and it satisfies the ACCP if every ascending ch…
Divisor sequences of atoms in Krull monoids
Nicholas R. Baeth, Terri Bell, Courtney R. Gibbons +1
The divisor sequence of an irreducible element (\textit{atom}) of a reduced monoid is the sequence where, for each positive integer , den…
Arithmetical invariants of local quaternion orders
Nicholas R. Baeth, Daniel Smertnig
Let be a DVR, let be its quotient field, and let be a -order in a quaternion algebra over . The elasticity of is $ρ(R^\bullet) = \sup\{\, k/l : u_…
A semigroup-theoretical view of direct-sum decompositions and associated combinatorial problems
Nicholas R. Baeth, Alfred Geroldinger, David J. Grynkiewicz +1
Let be a ring and let be a small class of right -modules which is closed under finite direct sums, direct summands, and isomorphisms. Let $\mathcal V (\mathcal…