Right ${\rm LCM}$ domains

Equilibrium States on Right Lcm Semigroup C-algebras

We determine the structure of equilibrium states for a natural dynamics on the boundary quotient diagram of C-algebras for a large class of right LCM semigroups. The approach is based on abstract properties of the semigroup and covers the previous case studies on N⋊N, dilation matrices, self-similar actions, and Baumslag– Solitar monoids. At the same time, it provides new results for large clas...

On the Smarandache LCM dual function

Received March 13, 2007 Abstract For any positive integer n, the Smarandache LCM dual function SL∗(n) is defined as the greatest positive integer k such that [1, 2, · · · , k] divides n. The main purpose of this paper is using the elementary method to study the calculating problem of a Dirichlet series involving the Smarandache LCM dual function SL∗(n) and the mean value distribution property o...

Digits in Lcm Upwrite Space

We inspect digit stroke sets in LCM UpWrite space.

Topological superconductor in quasi-one-dimensional ${\rm Tl}_{2-x}{\rm Mo}_6{\rm Se}_6$

Strong divisibility and lcm-sequences

Let R be an integral domain in which every two nonzero elements have a greatest common divisor. Let (an)n>1 be a sequence of nonzero elements in R. We prove that gcd(an, am) = agcd(n,m) for all n,m > 1 if and only if an = ∏