Abstract
We continue the theory of T-systems from the work of the second author, describing both ground systems and systemic modules over a ground system (paralleling the theory of modules over an algebra). The theory, summarized categorically at the end, encapsulates general algebraic structures lacking negation but possessing a map resembling negation, such as tropical algebras, hyperfields and fuzzy rings. We see explicitly how it encompasses tropical algebraic theory and hyperfields.
| Original language | English |
|---|---|
| Pages (from-to) | 221-270 |
| Number of pages | 50 |
| Journal | Contemporary Mathematics |
| Volume | 751 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Publisher Copyright:© 2020 American Mathematical Society.
Keywords
- Algebraic
- Bipotent
- Category
- Congruence
- Congruence
- Dimension
- Hyperfield
- Hypergroup
- Matroid
- Meta-tangible
- Module
- Negation
- Polynomial
- Prime
- Pseudo-system
- Pseudo-triple
- Semifield
- Semiring
- Supertropical algebra
- Surpassing relation
- Symmetrization
- Symmetrized
- System
- Tensor product
- Triple
- Tropical algebra