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The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1] The word problem on free Heyting algebras is ...
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods ...
This operation is known as reduction, and it does not change the group element represented by the word. Reductions can be thought of as relations (defined below) that follow from the group axioms. A reduced word is a word that contains no redundant pairs. Any word can be simplified to a reduced word by performing a sequence of reductions:
Microsoft Word is a word processing program developed by Microsoft.It was first released on October 25, 1983, [11] under the name Multi-Tool Word for Xenix systems. [12] [13] [14] Subsequent versions were later written for several other platforms including: IBM PCs running DOS (1983), Apple Macintosh running the Classic Mac OS (1985), AT&T UNIX PC (1985), Atari ST (1988), OS/2 (1989 ...
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes the class of groups as an object of study.
Scientific WorkPlace (often abbreviated to SWP) is a software package for scientific word processing on Microsoft Windows and macOS.. Although advertised as a WYSIWYG LaTeX-based word processor, it is actually a graphical user interface for editing LaTeX source files with the same ease-of-use of a word processor, while maintaining a screen view that resembles but is not identical to the ...
The term "algebra" is sometimes used in a more narrow sense to refer only to elementary algebra or only to abstract algebra. [14] When used as a countable noun , an algebra is a specific type of algebraic structure that involves a vector space equipped with a certain type of binary operation . [ 15 ]
Makes the content italicised and the same sans-serif font as normal text. Boolean: optional: Quotes? quotes q: Use 'yes' or any non-blank value to add quotation marks around the text. Boolean: optional