Open AccessSemiring Structures of Some Classes of Hypercodes
Author(s) -
ZhiXi Wang,
Feixiang Liang,
Yong He,
Yang Di
Publication year - 2009
Publication title -
justus-liebig-universität gießen
Language(s) - English
DOI - 10.25596/jalc-2009-259
Subject(s) - semiring , subvariety , idempotence , mathematics , monoid , variety (cybernetics) , free algebra , combinatorics , class (philosophy) , kleene algebra , order (exchange) , alphabet , set (abstract data type) , algebra over a field , pure mathematics , discrete mathematics , computer science , algebra representation , cellular algebra , linguistics , finance , economics , artificial intelligence , statistics , philosophy , programming language
An idempotent semiring is called an incline if it satisfies the identity 1 + x = x. The class of inclines is a variety of semirings with the variety of c-semirings as a subvariety. Let A* be the free monoid on an alphabet A, and let ≤h be the embedding order on A*. Then, as the algebra of independent subsets of the ordered monoid (A*, ≤h). the set H(A) of hypercodes on A forms a free incline. Furthermore, some subsets Hc (A) and Hmic (A) of H(A) can be constructed as a free c-semiring and a free multiplicatively idempotent c-semiring, respectively.
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