On generalized topological divisors of zero
نویسندگان
چکیده
منابع مشابه
Homology of zero-divisors
Let R be a commutative ring with unity. The set Z(R) of zero-divisors in a ring does not possess any obvious algebraic structure; consequently, the study of this set has often involved techniques and ideas from outside algebra. Several recent attempts, among them [2], [3] have focused on studying the so-called zero-divisor graph ΓR, whose vertices are the zero-divisors of R, with xy being an ed...
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In an algebra class, one uses the zero-factor property to solve polynomial equations. For example, consider the equation x 2 = x. Rewriting it as x (x − 1) = 0, we conclude that the solutions are x = 0, 1. However, the same equation in a different number system need not yield the same solutions. For example, in Z 6 (the integers modulo 6), not only 0 and 1, but also 3 and 4 are solutions. (Chec...
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AdigraphC is called a zero divisor if there exist non-isomorphic digraphs A and B for which A×C ∼= B ×C , where the operation is the direct product. In other words,C being a zero divisormeans that cancellation property A×C ∼= B×C ⇒ A ∼= B fails. Lovász proved that C is a zero divisor if and only if it admits a homomorphism into a disjoint union of directed cycles of prime lengths.Thus any digra...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1987
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-85-2-137-148