On a Condition for Semirings to Induce Compact Information Algebras | Zendy

Xuechong Guan | Zendy; Yongming Li | Zendy

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On a Condition for Semirings to Induce Compact Information Algebras

Author(s) -

Xuechong Guan,

Yongming Li

Publication year - 2014

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2014.01.004

Subject(s) - semiring , mathematics , kleene algebra , lattice (music) , algebraic structure , algebraic number , pure mathematics , algebra over a field , discrete mathematics , physics , mathematical analysis , acoustics

In this paper we study the relationship between ordering structures on semirings and semiring-induced valuation algebras. We show that a semiring-induced valuation algebra is a complete (resp. continuous) lattice if and only if the semiring is complete (resp. continuous) lattice with respect to the reverse order-relation on semirings. Furthermore, a semiring-induced information algebra is compact, if the dual of the semiring is an algebraic lattice

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