FACTOID # 10: The total number of state executions in 2005 was 60: 19 in Texas and 41 elsewhere. The racial split was 19 Black and 41 White.

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Encyclopedia > Center of a ring

The term center is used in various contexts in abstract algebra to denote the set of all those elements that commute with all other elements. More specifically: Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ... See: commuting commutative (mathematical) operation This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...

• The center of a group G consists of all those elements x in G such that xg = gx for all g in G. This is a normal subgroup of G.
• The center of a ring R is the subset of R consisting of all those elements x of R such that xr = rx for all r in R. The center is a commutative subring of R, so R is an algebra over its center.
• The center of an algebra A consists of all those elements x of A such that xa = ax for all a in A. See also: central simple algebra.
• The center of a Lie algebra L consists of all those elements x in L such that [x,a] = 0 for all a in L. This is an ideal of the Lie algebra L.

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 Why a Ring? (5316 words) To avoid designating some one ring node as special (and thereby making ring operation depend on that node's continued good health) some algorithm is required whereby all active repeaters can quickly and simply agree upon the need for initialization and recovery, and not fall all over one another trying to accomplish it. ring network were compared by measuring the board area required to hold the implementation of the network control logic up to but not including speed-matching buffers. In a token-controlled ring, an error may destroy the token at the worst possible time, or when a station nearing a deadline finally receives the token the message it sends may be damaged by an error, and retransmission may be needed.
 Ring (mathematics) - Wikipedia, the free encyclopedia (1407 words) A ring is a generalization of the integers. Rings that also satisfy commutativity for multiplication (such as the ring of integers) are called commutative rings. The center of a ring R is the set of elements of R that commute with every element of R; that is, c lies in the center if cr=rc for every r in R.
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