5 papers
The finite basis problem and subvariety intervals for max-plus matrix semirings
Jun Jiao, Mengya Yue
Let be the max-plus algebra of the nonnegative integers, and let be obtained from by adjoining as a semiring zero. We first prove that t…
Matrix varieties over : dimension-three stability and continuum-sized subvariety intervals
Jun Jiao, Xiaolei Shao
We study matrix semirings over the three-element flat additively idempotent semiring with elements one, a, and infinity, where the square of a is infinity. We determine the associa…
The finite basis problem for triangular Boolean matrix semirings and incidence semirings
Jun Jiao, Xiaolei Shao
An explicit finite identity basis is given for the eight-element semiring of upper triangular Boolean \(2\times2\) matrices in the signature \((+,\cdot)\). The basis consists of a…
The finite basis problem for matrix semirings
Jun Jiao, Miaomiao Ren
We first prove that two matrix semirings and are equationally equivalent whenever additively idempotent semirings and are equati…
The finite basis problem for matrix semirings over a two-element additively idempotent semiring
Jun Jiao, Miaomiao Ren
We provide a complete classification of matrix semirings over two-element additively idempotent semirings with respect to the finite basis property.Our main t…