On finitely generated subsemigroups of a free semigroup.
On finiteness conditions for Rees matrix semigroups
Let be a Rees matrix semigroup where is a semigroup, and are index sets, and is a matrix with entries from , and let be the ideal generated by all the entries of . If has finite index in , then we prove that is periodic (locally finite) if and only if is periodic (locally finite). Moreover, residual finiteness and having solvable word problem are investigated.
On Fitting Formations.
On fixed points of automorphisms of non-orientable unbordered Klein surfaces.
On Free Commutative Groupoids
On free commutative groupoids.
On free inverse monoid languages
On free products of bands.
On free products of bicyclic monoids.
On free subgroups of generalized triangle groups.
On free subgroups of units in quaternion algebras
It is well known that for the ring H(ℤ) of integral quaternions the unit group U(H(ℤ) is finite. On the other hand, for the rational quaternion algebra H(ℚ), its unit group is infinite and even contains a nontrivial free subgroup. In this note (see Theorem 1.5 and Corollary 2.6) we find all intermediate rings ℤ ⊂ A ⊆ ℚ such that the group of units U(H(A)) of quaternions over A contains a nontrivial free subgroup. In each case we indicate such a subgroup explicitly. We do our best to keep the arguments...
On free subgroups of units in quaternion algebras II
Let A ⊆ ℚ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra H(A) to units of certain rings of generalized quaternions H(A,a,b) = ((-a,-b)/A), where a,b ∈ A. Next we show that there is an algebra embedding of the ring H(A,a,b) into the algebra of standard Cayley numbers over A. Using this embedding we answer a question asked in the first part of this paper.
On free subsemigroups.
On Frobenius groups containing an element of order 3.
On Fuchs' problem 76.
On full partial quasigroups of finite order and local cardinal maximum codes.
On full transformation semigroups.
On fully unsaturated homomorphs of finite groups
On fuzzy points in semigroups.
On Galois covers of Hirzebruch surfaces.