## On general primarities which are equivalent to primality and tertiarity.(Russian)Zbl 0628.06008

Let L and R be complete lattices. L is called a lattice of operators of R if for any $$a\in R$$ and $$x\in L$$ the product xa$$\in R$$ is defined, such that xa$$\leq a$$, $$x(a+b)=xa+ya$$, $$(x+y)a=xa+xb$$ (where $$b\in R$$, $$y\in L)$$. For a modular lattice R (which satisfies some additional conditions), primarity is a map $$s: R\to L$$, such that $$s(1)=1$$, and for any $$a\in R$$, $$a\neq 1$$, $$r(a,s(a))>a$$, where $$r(a,x)=\sup \{b:$$ $$b\in R$$, xb$$\leq a\}$$. The author proves equivalence criteria to some special kind of primarity, which are useful for classification of primarities.
Reviewer: V.Meskhi

### MSC:

 06C05 Modular lattices, Desarguesian lattices 06B23 Complete lattices, completions
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