# maximality

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**maximality**— … Useful english dictionary**Compact operator on Hilbert space**— In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… … Wikipedia**Central carrier**— In the context of von Neumann algebras, the central carrier of a projection E is the smallest central projection, in the von Neumann algebra, that dominates E . It is also called the central supporting projection or central cover. Definition Let… … Wikipedia**Hausdorff maximal principle**— In mathematics, the Hausdorff maximal principle, (also called the Hausdorff maximality theorem) formulated and proved by Felix Hausdorff in 1914, is an alternate and earlier formulation of Zorn s lemma and therefore also equivalent to the axiom… … Wikipedia**Free abelian group**— In abstract algebra, a free abelian group is an abelian group that has a basis in the sense that every element of the group can be written in one and only one way as a finite linear combination of elements of the basis, with integer coefficients … Wikipedia**Boolean prime ideal theorem**— In mathematics, a prime ideal theorem guarantees the existence of certain types of subsets in a given abstract algebra. A common example is the Boolean prime ideal theorem, which states that ideals in a Boolean algebra can be extended to prime… … Wikipedia**Ideal (order theory)**— In mathematical order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal of abstract algebra, it has subsequently been generalized to a different… … Wikipedia**Field (mathematics)**— This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it … 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**Sylow theorems**— In mathematics, specifically group theory, the Sylow theorems, named after Ludwig Sylow, form a partial converse to Lagrange s theorem, which states that if H is a subgroup of a finite group G , then the order of H divides the order of G . The… … Wikipedia