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An element a of a ring which is nonzero, not a unit, and whose only divisors are the trivial ones (i.e., the units and the products ua, where u is a unit). Equivalently, an ...

A proper ideal of a ring that is not the intersection of two ideals which properly contain it. In a principal ideal domain, the ideal I=<a> is irreducible iff a=0 or a is an ...

A ring in which the zero ideal is an irreducible ideal. Every integral domain R is irreducible since if I and J are two nonzero ideals of R, and a in I, b in J are nonzero ...

A submodule N of a module M that is not the intersection of two submodules of M in which it is properly contained. In other words, for all submodules N_1 and N_2 of M, N=N_1 ...

An algebraic variety is called irreducible if it cannot be written as the union of nonempty algebraic varieties. For example, the set of solutions to xy=0 is reducible ...

If p divides the numerator of the Bernoulli number B_(2k) for 0<2k<p-1, then (p,2k) is called an irregular pair. For p<30000, the irregular pairs of various forms are p=16843 ...

A line making equal angles with the edges of a trihedron is called an isoclinal line of the trihedron.

A plane making equal angles with the three edges of a trihedron.

Two groups G and H are said to be isoclinic if there are isomorphisms G/Z(G)->H/Z(H) and G^'->H^', where Z(G) is the group center of the group, which identify the two ...

A rational homomorphism phi:G->G^' defined over a field is called an isogeny when dimG=dimG^'. Two groups G and G^' are then called isogenous if there exists a third group ...