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In a recent paper (Diversity in Monoids, Czech. Math. J. 62 (2012), 795–809), the last two authors introduced and developed the monoid invariant “diversity” and related properties “homogeneity” and “strong homogeneity”. We investigate these properties within the context of inside factorial monoids, in which the diversity of an element counts the number of its different almost primary components. Inside factorial monoids are characterized via diversity and strong homogeneity. A new invariant complementary...

Diversity in monoids

Jack Maney, Vadim Ponomarenko (2012)

Czechoslovak Mathematical Journal

Let $M$ be a (commutative cancellative) monoid. A nonunit element $q \in M$ is called almost primary if for all $a, b \in M$ , $q ∣ a b$ implies that there exists $k \in ℕ$ such that $q ∣ a^{k}$ or $q ∣ b^{k}$ . We introduce a new monoid invariant, diversity, which generalizes this almost primary property. This invariant is developed and contextualized with other monoid invariants. It naturally leads to two additional properties (homogeneity and strong homogeneity) that measure how far an almost primary element is from being primary. Finally, as an application...

Divisibility of integer polynomials and tilings of the integers

András Biró (2005)

Acta Arithmetica

Displaying 1 – 11 of 11

Davenport constant with weights and some related questions.

Decimal expansion of $1 / p$ and subgroup sums.

Decomposing rational numbers

Deriving divisibility theorems with Burnside's theorem.

Difference density and aperiodic sum-free sets.

Digraphs Associated With Finite Rings

Discrepancy of sums of three arithmetic progressions.

Disjoint Beatty sequences.

Diversity in inside factorial monoids

Diversity in monoids

Divisibility of integer polynomials and tilings of the integers

Currently displaying 1 – 11 of 11