# Semirings and their applications pdf

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Tropical linear algebra and its applications. Application and. The Rome-Moscow school of. Matrix Methods and Applied Linear Algebra.

## Semirings and their Applications

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## Semirings and their Applications

Algebraic number theory. Noncommutative algebraic geometry. In abstract algebra , a semiring is an algebraic structure similar to a ring , but without the requirement that each element must have an additive inverse. The term rig is also used occasionally [1] —this originated as a joke, suggesting that rigs are ri n gs without n egative elements, similar to using rng to mean a r i ng without a multiplicative i dentity. Tropical semirings are an active area of research, linking algebraic varieties with piecewise linear structures. Compared to a ring , a semiring omits the requirement for inverses under addition; that is, it requires only a commutative monoid , not a commutative group. In a ring, the additive inverse requirement implies the existence of a multiplicative zero, so here it must be specified explicitly.

## Semirings and their applications

Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available. Semirings and their Applications. Front Matter Pages i-xi.

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. When that book went out of print, it became clear - in light of the significant advances in semiring theory over the past years and its new important applications in such areas as idempotent analysis and the theory of discrete-event dynamical systems - that a second edition incorporating minor changes would not be sufficient and that a major revision of the book was in order. In particular, references to many interesting and applications of semiring theory, developed in the past few years, had to be added. Unfortunately, I find that it is best not to go into these applications in detail, for that would entail long digressions into various domains of pure and applied mathematics which would only detract from the unity of the volume and increase its length considerably.