On the cardinality of smallest spanning sets of rings

  • Nadia Boudi Département de Mathématiques, Faculté des Sciences, B.P. 2121, Tétouan, Marocco
  • Lorenz Halbeisen Department of Pure Mathematics, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland

Abstract

Let R = (R, +, ·) be a ring. Then ZR is called spanning if the R-module generated by Z is equal to the ring R. A spanning set ZR is called smallest if there is no spanning set of smaller cardinality than Z. It will be shown that the cardinality of a smallest spanning set of a ring R is not always decidable. In particular, a ring R = (R, +, ·) will be constructed such that the cardinality of a smallest spanning set ZR depends on the underlying set theoretic model.
Mathematics Subject Classification (2000): 13A18, 03E35
Key words: Spanning sets of rings, dominating number, bounding number

Quaestiones Mathematicae 26(2003), 321325
Published
2004-05-20
Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606