notions of the theory of rings; see J.Lambek [1 <...> otients of a commutative ring K is denoted by Q(K). We call K rationally complete if Q(K) K canonically or, equivalently, every irreducible fraction has domain K. Given a subset A of a commutative ring K, defi <...> deals of the form A∗ are called annihilator ideals. Thus J is an annihilator ideal if and only if J = A∗ for some subset A of K, and this is equivalent to saying that J∗∗ := (J∗)∗ = J. A commutative ring K is called semiprime if its prime radical is <...> 0, that is if it has no nonzero nilpotent elements. The annihilator ideals in a commutative semiprime ring K form a complete Boolean algebra A(K), with inters <...> only Archimedean f-rings. See more details in [2]. For a unital f-ring K the complete ring of quotients Q(A) can be <...>
Владикавказский_математический_журнал_№2_2015.pdf
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