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.
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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.
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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
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DOI: https://doi.org/10.1007/978-0-8176-4642-4_2
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Publisher Name: Birkhäuser, Boston, MA
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Online ISBN: 978-0-8176-4642-4
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