We establish virtual surjection to pairs (VSP) as a general criterion for the finite presentability of subdirect products of groups: if Γ1, . . . ,Γn are finitely presented and S < Γ1×· · ·×Γn projects to a subgroup of finite index in each Γi × Γj , then S is finitely presentable, indeed there is an algorithm that will construct a finite presentation for S. We use the VSP criterion to character...

Lattice of subquasivarieties of variety generated by modular ortholattices MOn, n 2 ! and MO! is described. In [3] Igo sin has proved that any subquasivariety of the variety M! is a variety. M! denoted variety generated by modular lattice M!, where M! is the lattice of length two with ! atoms. For short proof of this fact see [2]. In this note we present an orthomodular counterpart of this resu...

where (a) denotes the two-sided ideal of R generated by a. Then J is the Jacobson radical [6 ] of R, and N is the radical of R as defined in [l]. It is well known that J = 0 if and only if R is isomorphic to a subdirect sum of primitive rings, and ^ = 0 if and only if R is isomorphic to a subdirect sum of simple rings with unit element. The above definitions of / and N suggest that it might be ...

We introduce the wedge product of two polytopes. The wedge product is described in terms of inequality systems, in terms of vertex coordinates as well as purely combinatorially, from the corresponding data of its constituents. The wedge product construction can be described as an iterated “subdirect product” as introduced by McMullen (1976); it is dual to the “wreath product” construction of Jo...