caa a22 4500 386385378 CHVBK 20180307112056.0 cr unu---uuuuu 161130e198907 xx s 000 0 eng 10.1017/S0305004100067943 doi S0305004100067943 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100067943 Cohen Stephen D. Department of Mathematics, University of Glasgow, Glasgow G12 8QW The function field abstract prime number theorem [Elektronische Daten] [Stephen D. Cohen] For arithmetical semigroups modelled on the positive integers, there is an ‘abstract prime number theorem' (see, for example, [1]). In order to study enumeration problems in the several arithmetical categories whose prototype instead is the ring of polynomials in an indeterminate over a finite field of order q, Knopfmacher[2, 3] introduced the following modification. An additive arithmetical semigroup G is a free commutative semigroup with an identity, generated by a countable set of ‘primes' P and admitting an integer-valued degree mapping ∂ with the properties (i) ∂(l) = 0,∂(p) > 0 for pP; (ii) ∂(ab) = ∂(a) + ∂(b) for all a, b in G; (iii) the number of elements in G of degree n is finite. (This number will be denoted by G(n).) Copyright © Cambridge Philosophical Society 1989 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/1(1989-07), 7-12 0305-0041 106:1<7 1989 106 PSP https://doi.org/10.1017/S0305004100067943 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100067943 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Cohen Stephen D. Department of Mathematics, University of Glasgow, Glasgow G12 8QW NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/1(1989-07), 7-12 0305-0041 106:1<7 1989 106 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge