Original Articles

ON AN ALGEBRAIZATION OF MEASURE THEORY. ABSTRACT SEMIRINGS

Published in: Quaestiones Mathematicae
Volume 9 , issue 1-4 , 1986 , pages: 393–441

DOI: 10.1080/16073606.1986.9632125

Author(s): Teo Sturm Department of Mathematics and Applied Mathematics, Republic of South Africa

Keywords: Primary O6A12 , 28A6O , Secondary O3G25 , O6A23 , O6D99 , O6E1O

Abstract

The concept of a semiring is introduced as a semilattice analogue of a semiring of sets. A detailed study of its embeddability into r-complete Boolean algebras is carried out. Some of its properties which are important from the standpoint of Measure Theory are elucidated. A representation of a semiring by a Semiring of sets is derived. A relation to implicative BCK-algebras is also mentioned.

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