Mathematics – General Mathematics
Scientific paper
2008-02-17
J. Algebra Universalis, Vol. 61, No 3-4, (2009), pp. 381-397
Mathematics
General Mathematics
17 pages, 2 figures
Scientific paper
The paper deals with $\Sigma-$composition of terms, which allows us to extend the derivation rules in formal deduction of identities. The concept of essential variables and essential positions of terms with respect to a set of identities is a key step in the simplification of the process of formal deduction. $\Sigma-$composition of terms is defined as replacement between $\Sigma$-equal terms. This composition induces $\Sigma R-$deductively closed sets of identities. In analogy to balanced identities we introduce and investigate $\Sigma-$balanced identities for a given set of identities $\Sigma$.
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