[permalink] [id link]
Any abelian group can be turned into a zero ring by defining the product of any two elements to be 0.
from
Wikipedia
Some Related Sentences
Any and abelian
Any one-dimensional Lie algebra over a field is abelian, by the antisymmetry of the Lie bracket.
Any Lie group G can be decomposed into discrete, simple, and abelian groups in a canonical way as follows.
* Any ( pre ) abelian category is finitely complete and finitely cocomplete.
Any cyclotomic extension ( for either definition ) is abelian.
Any abelian variety is isogenous to a product of simple abelian varieties.
A weight on a Lie algebra g over a field F is a linear map λ: g → F with λ ( y )= 0 for all x, y in g. Any weight on a Lie algebra g vanishes on the derived algebra and hence descends to a weight on the abelian Lie algebra g /.
* Any finite abelian group, with the discrete topology.
* 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 semisimple Lie algebra or abelian Lie algebra is a fortiori reductive.
The theorem states: Any linearly ordered abelian group can be embedded as an ordered subgroup of the additive group ℝ < sup > Ω </ sup > endowed with a lexicographical order, where ℝ is the additive group of real numbers ( with its standard order ), and Ω is the set of Archimedean equivalence classes of.
Any abelian von Neumann algebra of operators on a separable Hilbert space is *- isomorphic to exactly one of the following
Any and group
* Any member of the genus Eunectes, a group of large, aquatic snakes found in South America
Any normal subgroup has a corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup.
Any formal or informal group — a family, a church, a club, a business, a trade union — may be said to have government.
* Any Lie group G defines an associated real Lie algebra.
* Any topologically closed subgroup of a Lie group is a Lie group.
* Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.
* Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1's on the diagonal of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.
# Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tangent vector to other points of the manifold.
" Any attempt to organize the group ... under a single authority would eliminate their independent initiatives, and thus reduce their joint effectiveness to that of the single person directing them from the centre.
Any symmetry group whose elements have a common fixed point, which is true for all finite symmetry groups and also for the symmetry groups of bounded figures, can be represented as a subgroup of orthogonal group O ( n ) by choosing the origin to be a fixed point.
However, in the case of a finitely presented group we know that not all the generators can be trivial ( Any individual generator could be, of course ).
* Any subgroup of a free group is free.
Any group of four students may run for office, but there must always be four students.
Any group that managed to find ways of reasoning effectively would reap benefits for all its members, increasing their fitness.
Any time during a triad conversation, group members can switch seats and one of the co-pilots can sit in the pilot ’ s seat.
Any group can be seen as a category with a single object in which every morphism is invertible ( for every morphism f there is a morphism g that is both left and right inverse to f under composition ) by viewing the group as acting on itself by left multiplication.
Any and can
He merely said, `` Any good decorator these days can make you a tasteful home ''.
Any alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.
Any reputable French interne can supply you with a dozen similar instances, and I'll presently recount a case out of my own personal experience, but, for the moment, let's resume our catalogue.
Any needy family living in San Francisco can obtain toys by writing to Christmas Toys, 676 Howard street, San Francisco 5, and listing the parent's name and address and the age and sex of each child in the family between the ages of 1 and 12.
Any breach of these laws is a criminal offence and can lead to fine of up to £ 5, 000 or six months in prison.
Any use of antibiotics can increase selective pressure in a population of bacteria to allow the resistant bacteria to thrive and the susceptible bacteria to die off.
* Any ring A can be considered as a Z-algebra in a unique way.
Any of these body styles can optionally incorporate a " cutaway ".
Any Latin-American country can join the 1980 Montevideo Treaty.
Any given bookmaker will weight their odds so that no one customer can cover all outcomes at a profit against their books.
Any node in the data structure can be reached by starting at root node and repeatedly following references to either the left or right child.
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.
Any of these ways can be criticized for ...
* Any locally compact Hausdorff space can be turned into a compact space by adding a single point to it, by means of Alexandroff one-point compactification.
Any Sangiovese-based wine made according to the Chianti guidelines from these vineyards can be labelled and marked under the basic Chianti DOCG should the producer wish to use the designation.
Any units of angular measure can be used for declination, but it is customarily measured in the degrees ( ° ), minutes ( ' ), and seconds ( " ) of sexagesimal measure, with 90 ° equivalent to circle.
Any convex polyhedron can be distorted into a canonical form, in which a midsphere ( or intersphere ) exists tangent to every edge, such that the average position of these points is the center of the sphere, and this form is unique up to congruences.
Any person who uses the Spanish title of " Doctor " ( or " Dr .") without being included in this Government database can be prosecuted for fraud.
Any player on the kicking team behind the kicker, and including the kicker, can recover the kick.
Any sound that can be sampled can be used.
Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters.
# Any real number can be added to both sides.
# Any real number can be subtracted from both sides.
# Any real number can be multiplied to both sides.
0.246 seconds.