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Semi-affine modes and modals. (English) Zbl 1067.08001
Summary: This paper is a survey of some selected topics from the theory of modes and modals. It is intended as an introduction to these topics, presenting basic facts and some background, discussion of the relations between the topics considered and their importance, information about current projects, and a list of open problems. The survey focuses primarily on the following concepts: idempotent (sub)reducts of semimodules over a commutative semiring, modes of submodes of a mode, modals, and representations and duality for modes and modals.

08-02 Research exposition (monographs, survey articles) pertaining to general algebraic systems
08A05 Structure theory of algebraic structures
16Y60 Semirings
06A12 Semilattices
08C05 Categories of algebras
52A01 Axiomatic and generalized convexity