A Logical Approach to Discrete Math pp 387-421 | Cite as

# Modern Algebra

## Abstract

*Modern algebra* is the study of the structure of certain sets along with operations on them. An *algebra* is basically a model of a theory, as discussed near the beginning of Chap. 9. The algebras discussed here are *semigroups, monoids, groups*, and *boolean algebras*. They are useful throughout computer science and mathematics. For example, Chap. 8 was devoted to the study of quantification over an arbitrary abelian monoid. Semigroups and monoids find application in formal languages, automata theory, and coding theory. And, one boolean algebra is the standard model of the propositional calculus. Important in our study is not only the various algebras but their interrelationship. Thus, we study topics like *isomorphisms, homomorphisms*, and *automorphisms* of algebras. (Historical note 18.1 discusses the origin of these words.)

## Keywords

Boolean Algebra Additive Group Binary Operator Propositional Calculus Prove Theorem## Preview

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