We introduce the notion of path extensions of tiling semigroups and investigate their properties. We show that the path extension of a tiling semigroup yields a strongly F *-inverse cover of the tiling semigroup and that it is isomorphic to an HNN * extension of its semilattice of idempo-tents.

We apply techniques from ω-stable and superstable groups to strongly connected and almost simple differential algebraic groups in the sense of Cassidy and Singer. We analyze differential algebraic group actions from this point of view, and prove several results regarding interpreting fields from these actions. We prove a differential algebraic analogue of Rienecke’s theorem. We show that every ...

Recently Swatee Naik and Theodore Stanford proved that two Sequivalent knots are related by a finite sequence of doubled-delta moves on their knot diagrams. We show that classical S-equivalence is not sufficient to extend their result to ordered links. We define a new algebraic relation on Seifert matrices, called Strong S-equivalence, and prove that two oriented, ordered links L and L are rela...

We prove that every small strongly connected category k has a full embedding preserving all limits existing in k into a category of unary universal algebras. The number of unary operations can be restricted to |mor k | in case when k has a terminal object and only preservation of limits over finitely many objects is desired. And all limits existing in such a category k are preserved by a full e...

We present an example of a zero-dimensional F-space that is not strongly zero-dimensional.