Commutative Semigroups Which Are Semigroup Amalgamation Bases

✍ Scribed by Kunitaka Shoji

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 371 KB
• Volume: 238
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8614

✦ Synopsis

α -r e 2 s at , and bt ≥ α 2i-r e 2 α -r e 2 s at . Since α r e 1 a ≥ e 1 at, there exists v ∈ S such that at = α r e 1 av. Then

e 1 sat . We can prove similarly the other inequations. Thus it follows from the equations above and Lemma 7(ii) that α 2i-r

α -r e 2 s at = α 2i-r f 2 α -r f 2 s at . Therefore α 2i-r e 1