On nilpotent subsemigroups of the matrix semigroup over an antiring

Yi-jia, Tan

doi:10.1016/j.laa.2011.04.013

Linear Algebra and its Applications

2011

DOI: 10.1016/j.laa.2011.04.013

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On nilpotent subsemigroups of the matrix semigroup over an antiring

Tan Yi-jia

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2015

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Maximal k-ideals and r-ideals in semirings

Han¹

2015

J. Algebra Appl.

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Communicated by J. RosenthalSome properties of (left) k-ideals and r-ideals of a semiring are considered by the help of the congruence class semiring. It is proved that a proper k-ideal of a semiring with an identity is prime if it is a maximal left k-ideal. An equivalent condition for a proper r-ideal of a semiring being a maximal (left) r-ideal is established. It is shown that (left) r-ideals and (left) k-ideals coincide for an additively idempotent semiring, though the former is a special kind of the latter in general. It is proved that a proper k-ideal of an incline with an identity is a maximal k-ideal if and only if the corresponding congruence class semiring is the Boolean semiring.

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Maximal k-ideals and r-ideals in semirings

Han¹

2015

J. Algebra Appl.

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On nilpotent subsemigroups of the matrix semigroup over an antiring

Cited by 1 publication

References 9 publications

Maximal k-ideals and r-ideals in semirings

Maximal k-ideals and r-ideals in semirings

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