Abstract: This chapter describes some ideals in universal algebras. If K is a variety of universal algebras having a nullary operation or equationally defined constant 0, then the notion of a 0-ideal for algebras in K can be generalized. The chapter presents some results concerning this concept mainly for the case when K is ideal-determined, which means that every 0-ideal is the class of 0 for exactly one congruence. It describes the generalization of this notion to get an f-ideal of A, where K is a variety, and A∈K and f is an arbitrary fundamental operation or a polynomial on A. The chapter further presents the notion of an f-normal subset of An+1, where f is n-ary, and also explores some of their properties and connections between them.
Publication Year: 1986
Publication Date: 1986-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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