Regular element
Encyclopedia
Regular element may refer to:
- In ring theoryRing theoryIn abstract algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers...
, a nonzero element of a ring that is neither a left nor a right zero divisorZero divisorIn abstract algebra, a nonzero element a of a ring is a left zero divisor if there exists a nonzero b such that ab = 0. 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 that is both a left and a right zero divisor is simply... - A regular element of a Lie algebraRegular element of a Lie algebraIn mathematics, a regular element of a Lie algebra or Lie group is an element whose centralizer has dimension as small as possible. For example, in the complex general linear group of nxn matrices, a diagonal matrix M will commute with its powers, and so with convergent series in those powers...
or Lie group.