On the additive structure of a class of ordered semirings. (English) Zbl 0582.06019
In this paper we determine the additive structure of totally ordered semirings if its multiplicative structure is a right naturally ordered o- Archimedean semigroup.
MSC:
| 06F25 | Ordered rings, algebras, modules |
| 16Y60 | Semirings |
| 20M25 | Semigroup rings, multiplicative semigroups of rings |
| 06F05 | Ordered semigroups and monoids |
| 16W80 | Topological and ordered rings and modules |
Keywords:
additive structure of totally ordered semirings; naturally ordered o- Archimedean semigroupReferences:
| [1] | L. Fuchs,Partially Ordered Algebraic Systems, Addison-Wesley Publishing Company, Inc. (1963). · Zbl 0137.02001 |
| [2] | M. Satyanarayana, Positively ordered semigroups,Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, Inc., Vol. 42 (1979). · Zbl 0411.06010 |
| [3] | M. Satyanarayana, Arcimedean property of ordered semirings,Semigroup Forum (submitted). |
| [4] | M. Satyanarayana and C. Srihari Nagore, Integrally ordered semigroups,Semigroup Forum, 17(1979), 101–111. · Zbl 0401.06008 · doi:10.1007/BF02194313 |
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