# ALGEBRAIC

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## ALGEBRAIC

(language)
An early system on MIT's Whirlwind.

[CACM 2(5):16 (May 1959)].

## algebraic

(theory)
In domain theory, a complete partial order is algebraic if every element is the least upper bound of some chain of compact elements. If the set of compact elements is countable it is called omega-algebraic.

References in periodicals archive ?
Several researchers (see Booth, 1988; Greeno, 1991; Kieran, 1992; Lins, 1990) suggest that many of the fundamental difficulties experienced by beginning algebra students are due to their failure to identify equivalent forms of an algebraic expression.
We say that a connected linear algebraic k-group G is k-split, or split over k, if its unipotent radical [R.
Additionally, when the functions are continuous, the values of x that satisfy f(x) = g(x) represent an algebraic way of determining the solutions of the inequations f(x) < g(x) and f(x) > g(x).
The neutrosophic algebraic structures are algebraic structures based on sets of neutrosophic numbers of the form N = a + bI, where a, b are real (or complex) numbers, and a is called the determinate part on N and bI is called the indeterminate part of N, with ml + ni = (m + n)I, 0-I = 0, I [conjunction] n = I for integer n [greater than or equal to] 1, and I / I = undefined.
The algebraic students are those who can; understand the functions, relations and patterns; present, analyse mathematical situations and structures; be able to construct and express mathematical model; and have the ability to analyze the variations in different contexts [Principles and Standards for Schools Mathematics, (2000)].
In Section 2, we give a few definitions, mostly illustrating the link between context-free grammars, solutions of positive algebraic systems and N-algebraic functions.
Also, in order to establish thoroughly the conceptual links needed for algebraic (and, in fact, all mathematical) thinking, "multiple representations" of the ideas are needed (Warren, 2003; Sfard, 1991).
By way of example, a typical pedagogical strategy is to suggest various equivalent algebraic expressions for the general term of a pictorial pattern.
AMS Special Session Algebraic Methods in Statistics and Probability (2d: 2009: Urbana-Champaign, IL) Ed.
The American Mathematical Society published details on how the Algebraic Eraser's key agreement protocol for public key cryptography is suitable for low resource devices, such as RFID tags, in their peer-reviewed book Algebraic Methods in Cryptography.
Research on the development of algebraic understanding by investigating the difficulties students encountered in solving algebraic problems has been well documented (Vlassis, 2002; Warren, 2003).
Section I, "The Nature of Algebraic Thinking," defines algebraic thinking and provides an argument for its development in the classroom.

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