One defines an equivalence relation on a commutative ring R by declaring elements r1, r2 ∈ R to be equivalent if and only if annR(r1) = annR(r2). If [r]R denotes the equivalence class of an element r ∈ R, then it is known that |[r]R| = |[r/1]T (R) |, where T(R) denotes the total quotient ring of R. In this paper, we investigate the extent to which a similar equality will hold when T(R) is replaced by Q(R), the complete ring of quotients of R. The results are applied to compare the zero-divisor graph of a reduced commutative ring to that of its complete ring of quotients.
von Neumann regular ring zero-divisor graph complete ring of quotients
Diğer ID | JA57SV42NC |
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Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 1 Aralık 2008 |
Yayımlandığı Sayı | Yıl 2008 Cilt: 4 Sayı: 4 |