According to a result by K. B. Lee, the lattice of varieties of pseudocomplemented distributive lattices is the ui + 1 chain B_i C Bo C Bi C • ■ ■ C Bn C •■ • C Bw in which the first three varieties are formed by trivial, Boolean, and Stone algebras respectively. In the present paper it is shown that any Stone algebra is determined within Bi by its endomorphism monoid, and that there are at mos...

We overview the logic of Bunched Implications (BI) and Separation Logic (SL) from a perspective inspired by Hiroakira Ono’s algebraic approach to substructural logics. We propose generalized BI algebras (GBI-algebras) as a common framework for algebras arising via “declarative resource reading”, intuitionistic generalizations of relation algebras and arrow logics and the distributive Lambek cal...

If the free algebra F on one generator in a variety V of algebras (in the sense of universal algebra) has a subalgebra free on two generators, must it also have a subalgebra free on three generators? In general, no; but yes if F generates the variety V. Generalizing the argument, it is shown that if we are given an algebra and subalgebras, A0 ⊇ · · · ⊇ An, in a prevariety (S P -closed class of ...

Abstract The graphical description of morphisms in rigid monoidal categories, in particular in ribbon categories, is summarized. It is illustrated with various examples of algebraic structures in such categories, like algebras, (weak) bi-algebras, Frobenius algebras, and modules and bimodules. Nakayama automorphisms of Frobenius algebras are introduced; they are inner iff the algebra is symmetric.

When combining languages for symbolic constraints, one is typically faced with the problem of how to treat \mixed" constraints. The two main problems are (1) how to deene a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint solving methods for pure constraints into one for mixed constraints. The paper introduces the notion of a \free...

We develop a theory which unifies the universal (co)acting bi/Hopf algebras as studied by Sweedler, Manin and Tambara with recently introduced \cite{AGV1} bi/Hopf-algebras that are among all support equivalent algebras. Our approach uses vector spaces endowed family of linear maps between tensor powers $A$, called $\Omega$-algebras. This allows us to treat algebras, coalgebras, braided many oth...

Every countable directed graph generates a Fock space Hilbert space and a family of partial isometries. These operators also arise from the left regular representations of free semigroupoids derived from directed graphs. We develop a structure theory for the weak operator topology closed algebras generated by these representations, which we call free semigroupoid algebras. We characterize semis...

We prove the conjectures on dimensions and characters of some quadratic algebras stated by B.L.Feigin. It turns out that these algebras are naturally isomorphic to the duals of the components of the bi-Hamiltonian operad.