Some collections of submodules of a module defined by certain conditions are studied. A generalization of the notion of radical (preradical) filter is considered. We study the form of filters of semisimple modules and direct sums.

We prove that varieties of (ℓr, rr)-dibands and (ℓn, rn)-dibands coincide and describe the structure of free (ℓr, rr)-dibands. We also show that operations of an idempotent dimonoid with left (right) regular bands coincide, ...

If G is a group with a presentation of the form ⟨x, y|x³ = yq = W(x, y)² = 1⟩, then either G is virtually soluble or G contains a free subgroup of rank 2. This provides additional evidence in favour of a conjecture of Rosenberger.

A convolution is a mapping C of the set Z⁺ of positive integers into the set P(Z⁺) of all subsets of Z⁺ such that every member of C(n) is a divisor of n. If for any n, D(n) is the set of all positive divisors of n, then D ...

The computation of the Möbius function of a Möbius category that arises from a combinatorial inverse semigroup has a distinctive feature. This computation is done on the field of finite posets. In the case of two combinatorial ...

The concept of graph structure was introduced by E. Sampathkumar in 'Generalised Graph Structures', Bull. Kerala Math. Assoc., Vol 3, No.2, Dec 2006, 65-123. Based on the works of Brouwer, Doob and Stewart, R.H. Jeurissen ...

It is given a short scientific biography of Professor L.A. Shemetkov.

It is proved that if π-Hall subgroup is a supersolvable group then the derived π-length of a π-solvable group G is at most 1 + maxr∈π lαr(G), where lαr(G) is the derived r-length of a π-solvable group G.

In this note we prove that the ring B²n has non-zero irreducible locally nilpotent derivations, which are explicitly presented, and that its ML-invariant is C.

The matching basis in field extentions is introduced by S. Eliahou and C. Lecouvey in [2]. In this paper we define the minimal and maximal linear matching property for field extensions and prove that if K is not algebraically ...