Congruence-simple multiplicatively idempotent semirings
Let S be a multiplicatively idempotent congruence-simple semiring. We show that | S | = 2 if S has a multiplicatively absorbing element. We also prove that if S is finite then either | S | = 2 or S ≅ End ( L ) or S op ≅ End ( L ) where L is the 2-element semilattice. It seems to be an open question,...
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| Veröffentlicht in: | Algebra universalis 2023-05, Vol.84 (2), Article 13 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
S
be a multiplicatively idempotent congruence-simple semiring. We show that
|
S
|
=
2
if
S
has a multiplicatively absorbing element. We also prove that if
S
is finite then either
|
S
|
=
2
or
S
≅
End
(
L
)
or
S
op
≅
End
(
L
)
where
L
is the 2-element semilattice. It seems to be an open question, whether
S
can be infinite at all. |
|---|---|
| ISSN: | 0002-5240 1420-8911 |
| DOI: | 10.1007/s00012-023-00807-7 |