Abstract
Let Z be the additive (semi)group of integers. We prove that for a finite semigroup S the direct product Z × S contains only countably many subdirect products (up to isomorphism) if and only if S is regular. As a corollary we show that Z × S has only countably many subsemigroups (up to isomorphism) if and only if S is completely regular.
Original language | English |
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Number of pages | 10 |
Journal | Bulletin of the Australian Mathematical Society |
Volume | First View |
Early online date | 4 Oct 2024 |
DOIs | |
Publication status | E-pub ahead of print - 4 Oct 2024 |
Keywords
- Direct product
- Subdirect product
- Subsemigroup
- Regular semigroup
- Completely regular semigroup