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A module is called flat if taking the tensor product of it with any exact sequence of R-modules preserves exactness. Torsionless A module is called torsionless if it embeds into its algebraic dual. Simple A simple module S is a module that is not {0} and whose only submodules are {0} and S. Simple modules are sometimes called irreducible. [5 ...
In coordination chemistry, a coordinate covalent bond, [1] also known as a dative bond, [2] dipolar bond, [1] or coordinate bond [3] is a kind of two-center, two-electron covalent bond in which the two electrons derive from the same atom. The bonding of metal ions to ligands involves this kind of interaction. [4]
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic [1] – do not vary smoothly in this way, but have distinct, separated values. [2]
Oxidation of R 3 P–M complexes results in longer M–P bonds and shorter P–C bonds, consistent with π-backbonding. [11] In early work, phosphine ligands were thought to utilize 3d orbitals to form M–P pi-bonding, but it is now accepted that d-orbitals on phosphorus are not involved in bonding as they are too high in energy. [12] [13]
[1]: 410–417 In VSEPR theory, a double bond or triple bond is treated as a single bonding group. [1] The sum of the number of atoms bonded to a central atom and the number of lone pairs formed by its nonbonding valence electrons is known as the central atom's steric number.
Bond order is the number of chemical bonds between a pair of atoms. The bond order of a molecule can be calculated by subtracting the number of electrons in anti-bonding orbitals from the number of bonding orbitals, and the resulting number is then divided by two. A molecule is expected to be stable if it has bond order larger than zero.
If the points are sequentially numbered and located at positions r 1, r 2, r 3, etc. then bond vectors are defined by u 1 = r 2 − r 1, u 2 = r 3 − r 2, and u i = r i+1 − r i, more generally. [2] This is the case for kinematic chains or amino acids in a protein structure. In these cases, one is often interested in the half-planes defined ...
In Organic chemistry, the inductive effect in a molecule is a local change in the electron density due to electron-withdrawing or electron-donating groups elsewhere in the molecule, resulting in a permanent dipole in a bond. [1] It is present in a σ (sigma) bond, unlike the electromeric effect which is present in a π (pi) bond.