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Page "Bimodule" ¶ 9
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Any and ideal
Any Banach algebra ( whether it has an identity element or not ) can be embedded isometrically into a unital Banach algebra so as to form a closed ideal of.
* Norton's theorem: Any network of voltage or current sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.
Any philosophy that assigns crucial importance to the ideal or spiritual realm in its account of human existence may be termed " idealist ".
Any form of triangle that we experience will be an imperfect representation of the ideal triangle.
* Any principal ideal domain, such as the integers, is Noetherian since every ideal is generated by a single element.
Any black box containing only voltage sources, current sources, and other resistors can be converted to a Norton equivalent circuit, comprising exactly one ideal current source and one resistor.
Any departure from this ideal harmonic series is known as inharmonicity.
Any quotient of a ring by a maximal ideal is a simple ring.
Any prime number p gives rise to an ideal pO < sub > K </ sub > in the ring of integers O < sub > K </ sub > of a quadratic field K.
Any component of an ideal solution obeys Raoult's Law over the entire composition range:
Any political party or faction that seeks to form a majority in a parliament or on a board of directors or other responsible body typically must run a full slate if only to demonstrate that they have the capacity to attract the talent to fill every position with some person, even if that person is not ideal for the job.
Any mixture less than 14. 7 to 1 is considered to be a rich mixture ; any more than 14. 7 to 1 is a lean mixture – given perfect ( ideal ) " test " fuel ( gasoline consisting of solely n-heptane and iso-octane ).
Any dissimilarity between the optical fields will decrease the visibility from the ideal.
Any subgroup of the additive group of a zero ring is an ideal.

Any and ring
* Any ring A can be considered as a Z-algebra in a unique way.
* Any ring of characteristic n is a ( Z / nZ )- algebra in the same way.
* Any ring A is an algebra over its center Z ( A ), or over any subring of its center.
* Any commutative ring R is an algebra over itself, or any subring of R.
* Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication.
* Any discrete valuation ring.
Any legal wrestler is open to attack from any direction at any time, including when they are downed, as long as they are within the ring area enclosed by the ring ropes.
Any type or number of topologies may be used -- star, bus, ring, etc.
* Any ring, thought of as a category with only one object, is a preadditive category.
Any ( non-graded ) ring A can be given a gradation by letting A < sub > 0 </ sub >
Any number system that forms a commutative ring — for instance, the integers, the real numbers, and the complex numbers — can be extended to a wheel in which division by zero is always possible ; however, in such a case, " division " has a slightly different meaning.
Any ring can be seen as a preadditive category with a single object.
* Any commutative ring becomes a *- ring with the trivial involution.
* Any ring is also a semiring.
* Any ring R can be considered as a one-object preadditive category ; the category of left modules over R is the same as the additive functor category Add ( R, Ab ) ( where Ab denotes the category of abelian groups ), and the category of right R-modules is Add ( R < sup > op </ sup >, Ab ).
* Any algebra over a commutative ring K may be regarded as a purely even superalgebra over K ; that is, by taking A < sub > 1 </ sub > to be trivial.
Any n-dimensional formal group law gives an n dimensional Lie algebra over the ring R, defined in terms of the quadratic part F < sub > 2 </ sub > of the formal group law.
* Any module over a commutative ring R is automatically a bimodule.

Any and R
Any subset of R < sup > n </ sup > ( with its subspace topology ) that is homeomorphic to another open subset of R < sup > n </ sup > is itself open.
Brown continued releasing recordings: in 1993, he issued the album, Universal James, which included Brown's final Billboard charted single, " Can't Get Any Harder ", which peaked at # 76 on the US R & B chart and # 59 on the UK chart.
Any formal series with has a composition inverse provided is an invertible element of R. The coefficients are found recursively from the above formula for the coefficients of a composition, equating them with those of the composition identity X ( that is 1 at degree 1 and 0 at every degree greater than 1 ).
* Any positive multiple of the repunit R < sub > n </ sub >< sup >( b )</ sup > contains at least n nonzero digits in base b.
Any binary relation R on a set A can generate a natural partial order on the R-cycle equivalence classes of set A, so that xRy implies ≥.
* The Drug War in Mexico: By Any Other Name it's Terrorism, by Barnard R. Thompson ( MexiData. info )
Any totally ordered set that is not isomorphic to R but satisfies ( 1 ) – ( 4 ) is known as a Suslin line.
Any physical object whose radius R becomes less than or equal to the Schwarzschild radius will undergo gravitational collapse and become a black hole.
Any proposed inverse R of F ( reconstruction formula, in the lingo ) would have to map to some subset of.
* Any slave who evades capture for 20 days or more is to be publicly whipped for the first offense ; branded with the letter R on the right cheek for the second offense ; and lose one ear if absent for thirty days for the third offense ; and castrated for the fourth offense.
In early June, Banks released the second single off the album, " Any Girl " featuring R & B singer Lloyd.
O. A. R., who grew up in nearby Rockville, Maryland, recorded the live album Any Time Now at the 9: 30 Club on November 23 – 24, 2001.
Any non-singular matrix S of the same size is said to transform A into another symmetric matrix B = SAS < sup > T </ sup >, also of order n, where S < sup > T </ sup > is the transpose of S. If A is the coefficient matrix of some quadratic form of R < sup > n </ sup >, then B is the matrix for the same form after the change of coordinates defined by S.
Lloyd C. Gardner, " Pay Any Price: Lyndon Johnson and the Wars for Vietnam ", Chicago: Ivan R. Dee, 1995.

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