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Quotient semigroup; extension semigroup; congruence relation.

We discuss properties of quotient semigroup of abelian semigroup from the viewpoint of 𝐶*-algebra and apply them to a survey of extension semigroups. Certain interrelations among some equivalence relations of extensions are also considered.

Rong Xing¹ Changguo Wei² Shudong Liu³

1. Department of Mathematics, Teachers College of Qingdao University, Qingdao 266071, People’s Republic of China
2. School of Mathematical Sciences, Ocean University of China, Qingdao 266100, People’s Republic of China
3. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, People’s Republic of China

Manuscript received

2 March 2011

Manuscript revised

23 May 2011