Discussiones Mathematicae General Algebra and Applications 24(2) (2004)
225-249
doi: 10.7151/dmgaa.1087
Qiang Wang
School of Mathematics and Statistics |
Shelly L. Wismath
Department of Mathematics and C.S. |
In this paper we define the concept of a generalized inflation for any type of algebra. In particular, we allow for generalized inflations of semigroups which are no longer semigroups themselves. After some general results about such generalized inflations, we characterize for several varieties of bands which null extensions of algebras in the variety are generalized inflations, and which of these are associative. These characterizations are used to produce examples which answer, in our more general setting, several of the open questions posed by Clarke and Monzo.
Keywords: inflation, generalized inflation, null extension, variety of semigroups, bands.
2000 Mathematics Subject Classification: 08A05, 20M07, 20M10.
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Received 17 May 2004
Revised 8 July 2004