An e-ring is a pair (R,E) consisting of an associative ring R with unity 1 together with a subset E ⊆ R of elements, called effects, with properties suggested by the so-called effect operators on a Hilbert space. We establish the basic properties of e-rings, investigate commutative e-rings called c-rings, relate certain c-rings called b-rings to Boolean algebras, and prove a structure theorem f...

We consider ω-automatic structures which are relational structures whose domain and relations are accepted by automata reading ordinal words of length ω for some integer n ≥ 1. We show that all these structures are ω-tree-automatic structures presentable by Muller or Rabin tree automata. We prove that the isomorphism relation for ω-automatic (resp. ω-automatic for n > 2) boolean algebras (respe...

Using the concept of the λ-lattice introduced recently by V. Snášel we define λ-lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.