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The free monoid on a set A is usually denoted A ∗. The free semigroup on A is the subsemigroup of A ∗ containing all elements except the empty string. It is usually denoted A +. [1] [2] More generally, an abstract monoid (or semigroup) S is described as free if it is isomorphic to the free monoid (or semigroup) on some set. [3]
Second, medical roots generally go together according to language, i.e., Greek prefixes occur with Greek suffixes and Latin prefixes with Latin suffixes. Although international scientific vocabulary is not stringent about segregating combining forms of different languages, it is advisable when coining new words not to mix different lingual roots.
In computer science and computer programming, the set of strings built from a given set of characters is a free monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation for process calculi and concurrent computing.
The main discussion of these abbreviations in the context of drug prescriptions and other medical prescriptions is at List of abbreviations used in medical prescriptions. Some of these abbreviations are best not used, as marked and explained here.
The monoid is then presented as the quotient of the free monoid (or the free semigroup) by these relations. This is an analogue of a group presentation in group theory . As a mathematical structure, a monoid presentation is identical to a string rewriting system (also known as a semi-Thue system).
Medical terminology is a language used to precisely describe the human body including all its components, processes, conditions affecting it, and procedures performed upon it. Medical terminology is used in the field of medicine .
Pronunciation follows convention outside the medical field, in which acronyms are generally pronounced as if they were a word (JAMA, SIDS), initialisms are generally pronounced as individual letters (DNA, SSRI), and abbreviations generally use the expansion (soln. = "solution", sup. = "superior").
Algebraic structures between magmas and groups: A semigroup is a magma with associativity.A monoid is a semigroup with an identity element.. In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it.