On multiplicative semigroups of residue classes

On Multiplicative Semigroups of Residue Classes

The set of residue classes, modulo any positive integer, is commutative and associative under the operation of multiplication. The author made the conjecture: For each finite commutative semigroup, S, there exists a positive integer, n, such that S is isomorphic with a subsemigroup of the multiplicative semigroup of residue classes (mod n). (A semigroup is a set closed with respect to a single-...

Multiplicative Functionals on Semigroups of Continuous Functions

Let X be a compact Hausdorff space. We denote by C(X) the multiplicative semigroup of all continuous real-valued functions on X. Milgram [2] has shown that C(X) as a semigroup determines X. In this paper we investigate the set %(X) of all continuous positive nontrivial2 multiplicative functionals on C(X), where C(X) has the topology of uniform convergence. If multiplication is defined pointwise...

Freeness of Multiplicative Matrix Semigroups

V. D. Blondel Department of Mathematical Engineering University of Louvain Avenue Georges Lemaitre, 4 B-1348 Louvain-la-Neuve Belgium Email: [email protected] J. Cassaigne Institut de Mathématiques de Luminy UPR 9016 Campus de Luminy, Case 907 13288 Marseille Cedex 9 France Email: [email protected] J. Karhumäki Dept. of Math. & TUCS University of Turku FIN-20014 Turku Finland Email: ...

Multiplicative diagonals of matrix semigroups

On the Basic Character of Residue Classes

ON THE BASIC CHARACTER OF RESIDUE CLASSES P . HILTON, J . HOOPER AND J . PEDERSEN Let t, b be mutually prime positive integers . We say that the residue class t mod b is basic if theie exists n such that ta -1 mod b; otherwise t is not basic. In this paper we relate the basic character of t mod b to the quadratic character of t modulo the prime factors of b. If all prime factors p of b satisfy ...