Abstract
This chapter provides background material; it has two sections. The first briefly introduces universal algebra. The second surveys the many ways that products of algebras may be captured both externally and internally.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Here is the reason for this name. The prefix ‘sesqui’ means a ratio of 3:2. When written with a sequence \(\vec{a}\) of elements of A, formula (ii) becomes \(\mu \big{(}\omega (\mu \circ \vec{ a})\big{)} = \mu \big{(}\omega (\vec{a})\big{)}\), with three occurrences of μas opposed to two in the formula for a homomorphism, \(\omega (\mu \circ \vec{ a}) = \mu \big{(}\omega (\vec{a})\big{)}\).
- 2.
The traditional term for relations is ‘permute’, but the preferred term in this book is ‘commute’ since other related notions, such as endomorphisms, traditionally commute.
- 3.
Swamy and Murti [SwaMu81a] discuss factor elements in semigroups, where they call them ‘central’ elements. Central elements are more generally defined as sequences of elements in [VagSá04] and [SánVa09]. There the origin and terminus become sequences of unary operations.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Knoebel, A. (2012). Algebra. In: Sheaves of Algebras over Boolean Spaces. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4642-4_2
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4642-4_2
Published:
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4218-1
Online ISBN: 978-0-8176-4642-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)