On several varieties of cacti and their relations.
In this paper we introduce the notion of the structure space of -semigroups formed by the class of uniformly strongly prime ideals. We also study separation axioms and compactness property in this structure space.
The aim of this paper is to develop the homological machinery needed to study amalgams of subrings. We follow Cohn [1] and describe an amalgam of subrings in terms of reduced iterated tensor products of the rings forming the amalgam and prove a result on embeddability of amalgamated free products. Finally we characterise the commutative perfect amalgamation bases.
We investigate the formal matrix ring over defined by a certain system of factors. We give a method for constructing formal matrix rings from non-negative integer matrices. We also show that the principal factor matrix of a binary system of factors determine the structure of the system.
Let be a finite group , a field of characteristic and let be the group of units in . We show that if the derived length of does not exceed , then must be abelian.