componentwise addition

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• Ordered group — In abstract algebra, an ordered group is a group (G,+) equipped with a partial order ≤ which is translation invariant ; in other words, ≤ has the property that, for all a , b , and g in G , if a ≤ b then a+g ≤ b+g and g+a ≤ g+b . Note that… …   Wikipedia

• Partially-ordered group — In abstract algebra, a partially ordered group is a group (G,+) equipped with a partial order ≤ that is translation invariant; in other words, ≤ has the property that, for all a, b, and g in G, if a ≤ b then a+g ≤ b+g and g+a ≤ g+b. An element x… …   Wikipedia

• Subring — In mathematics, a subring is a subset of a ring, which contains the multiplicative identity and is itself a ring under the same binary operations. Naturally, those authors who do not require rings to contain a multiplicative identity do not… …   Wikipedia

• Zero divisor — In abstract algebra, a nonzero element a of a ring is a left zero divisor if there exists a nonzero b such that ab = 0.[1] Similarly, a nonzero element a of a ring is a right zero divisor if there exists a nonzero c such that ca = 0. An element… …   Wikipedia

• Baer–Specker group — In mathematics, in the field of group theory, the Baer–Specker group, or Specker group, is an example of an infinite Abelian group which is a building block in the structure theory of such groups.DefinitionThe Baer Specker group is the group B =… …   Wikipedia

• Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

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• Direct sum of modules — For the broader use of the term in mathematics, see Direct sum. In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The result of the direct summation of modules is the smallest general… …   Wikipedia

• Direct product of groups — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• Direct product — In mathematics, one can often define a direct product of objects already known, giving a new one. This is generally the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one… …   Wikipedia

• Hyperreal number — *R redirects here. For R*, see Rockstar Games. The system of hyperreal numbers represents a rigorous method of treating the infinite and infinitesimal quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R… …   Wikipedia