References
M. A. Arbib and E. G. Manes, Partially-additive categories and flow-diagram semantics, Journal of Algebra62, 1980, 203–227.
M. A. Arbib and E. G. Manes, The pattern-of-calls expansion is the canonical fixpoint for recursive definitions, Journal of the Association for Computing Machinery29, 1982, 557–602.
J. W. Backus, Can programming be liberated from the von Neumann style? A functional style and its algebra of programs, Communications of the Association for Computing Machinery21, 1978, 613–641.
D. B. Benson, Counting paths: nondeterminism as linear algebra, to appear in IEEE Trans. Soft Eng., Nov. 1984.
G. Birkhoff, Lattice Theory, American Mathematical Society Colloquium Publications25, revised edition, American Mathematical Society, New York, 1967.
N. Bourbaki, General Topology, Part 1, Addison-Wesley, 1966.
S. Eilenberg, Automata, Languages and Machines, Academic Press, 1974.
D. Higgs, Axiomatic infinite sums—an algebraic approach to integration theory, Contemporary Mathematics2, 1980, 205–212.
J. M. Howie, An Introduction to Semigroup Theory, Academic Press, 1976.
B. Mahr, Semirings and transitive closure, Bericht Nr. 82-5, Fachbereich 20, Technical University of Berlin, 1982, 84pp.
E. G. Manes, A class of fuzzy theories, Journal of Mathematical Analysis and its Applications85, 1982, 409–451.
E. G. Manes and M. A. Arbib, Algebraic Approaches to Program Semantics, Springer-Verlag, to appear.
Z. Manna, Mathematical Theory of Computation, McGraw-Hill, 1974.
D. B. McAlister, Amenably ordered inverse semigroups, Journal of Algebra65, 1980, 118–146.
D. S. Scott, The lattice of flow diagrams, in Symposium on Semantics of Algorithmic Languages, Lecture Notes in Mathematics188, E.Engeler (Ed.), Springer-Verlag, 1971, 311–366.
U. M. Swamy and G. S. Murti, Boolean centre of a semigroup, Pure and Applied Mathematika Sciences13, 1981, No. 1-2, 5–6.
A. Tarski, Cardinal Algebras, Oxford University Press New York, 1949.
Author information
Authors and Affiliations
Additional information
Communicated by G. Lallement
Research partially supported by National Science Foundation grants MCS-8205168 and MCS-8003433.
Rights and permissions
About this article
Cite this article
Manes, E.G., Benson, D.B. The inverse semigroup of a sum-ordered semiring. Semigroup Forum 31, 129–152 (1985). https://doi.org/10.1007/BF02572645
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02572645