Premium
Converse Prime Element Theorems for Arithmetical Semigroups
Author(s) -
Warlimont Richard
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200204)237:1<147::aid-mana147>3.0.co;2-o
Subject(s) - mathematics , arithmetic function , converse , multiplicative function , semigroup , prime factor , element (criminal law) , multiplicity (mathematics) , multiplicative number theory , prime (order theory) , pure mathematics , discrete mathematics , arithmetic , combinatorics , mathematical analysis , geometry , political science , law
Conditions are presented which ensure that in an additive (multiplicative) arithmetical semigroup a positive proportion of all elements are prime elements. Under these conditions asymptotics are derived for the average number of elements with a fixed number of prime element factors, counted with and without multiplicity.