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(əˈbi li ən, əˈbil yən)

of or pertaining to an algebraic system in which an operation is commutative.
[1905–10; after Niels Henrik Abel (1802–29), Norwegian mathematician]
References in periodicals archive ?
Among their topics are isonoetherian and isoartinian modules, the universal abelian regular ring, a characterization of t-tilting finite algebras, multisorted modules and their module theory, pure projective modules over non singular serial rings, and intrinsic valuation entropy.
Treating electric flux lines as the dynamical degrees of freedom of gauge theories leads to a representation of Wilson loop associated with a closed curve C for Abelian gauge theories.
Our paper [OO] is a sequel to a series by the first author [Od14, Od18], which compactified both the moduli space of compact Riemann surfaces [M.sub.g](g [greater than or equal to] 2) and that of principally polarized abelian varieties [A.sub.g].
On products of cyclic and abelian finite p-groups (p odd) ...
Furthermore, we have demonstrated the existence of such (i.e., (anti-)co-BRST) symmetries in the cases of Abelian p-form (p = 1,2,3) gauge theories in the two (1 + 1) dimensions, four (3+1) dimensions, and six (5 + 1) dimensions of spacetime (see, e.g., [18] and references therein).
Dhompongsa [5] proved that each infinite dimensional unital Abelian real Banach algebra X with [OMEGA](X) [not equal to] 0 satisfying (i) if x, y [member of] X is such that [absolute value of [tau](x)] [less than or equal to] [absolute value of [tau](y)] for each [tau] [member of] [OMEGA](X) then [parallel]x[parallel] [less than or equal to] [parallel]y[parallel] and (ii) inf {r(x) : x [member of] X, [parallel]x[parallel] = 1} > 0 does not have the fixed point property.
Abelian anyons have been detected and play a major role in the fractional quantum Hall effect.
Let [C.sub.r](A) be the free abelian group generated by the set [[DELTA].sub.r](A) consisting of all elements of the form ([a.sub.1],...,[a.sub.r],[[gamma].sub.1],...,[[gamma].sub.r]) where [a.sub.1],...,[a.sub.r] are pairwise distinct elements of A, and [[gamma].sub.1],...,[[gamma].sub.r] are any elements of [GAMMA]; in particular, [C.sub.r](A) = Z if r = 0.
More precisely, for a field k, a joint determinant D (= [D.sub.l]) (l [greater than or equal to] 1) is defined as a map from the set of l-tuples of commuting matrices in [GL.sub.n](k) (n [greater than or equal to] 1) into some abelian group (G, +) which satisfies the following properties.
Let H be a finite abelian group written additively and End(H) be the endomorphism ring of H.
It is well known that all endomorphisms of an Abelian group form a ring and many of its properties can be characterized by this ring.
These results on Euclidean self-dual cyclic codes have been generalized to abelian codes in group algebras [6] and the complete characterization and enumeration of Euclidean self-dual abelian codes in principal ideal group algebras (PIGAs) have been established.