Universal algebra [5, 9, 4] is the theory of equalities t = u. It is a simple framework within which we can study mathematical structures, for example groups, rings, and fields. It has also been applied to study the mathematical properties of mathematical truth and computability. For example boolean algebras correspond to classical truth, heyting algebras correspond to intuitionistic truth, cyl...

FLew-algebras form the algebraic semantics of the full Lambek calculus with exchange and weakening. We investigate two relations, called satisfiability and positive satisfiability, between FLew-terms and FLew-algebras. For each FLew-algebra, the sets of its satisfiable and positively satisfiable terms can be viewed as fragments of its existential theory; we identify and investigate the compleme...

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point ...

The dual of the category of pointed objects of a topos is semiabelian, thus is provided with a notion of semi-direct product and a corresponding notion of action. In this paper, we study various conditions for representability of these actions. First, we show this to be equivalent to the existence of initial normal covers in the category of pointed objects of the topos. For Grothendieck toposes...

We find an order-theoretic characterization of the Lindenbaum algebra of intuitionistic propositional logic in n variables and in countably infinitely many variables. The poset of join-irreducibles in countably infinitely many variables is proved to be a Fräissé limit of an order-theoretic class of structure.

We introduce Brauer complex of symmetric SB-algebra, and reformulate in terms of Brauer complex the so far known invariants of stable and derived equivalence of symmetric SB-algebras. In particular, the genus of Brauer complex turns out to be invariant under derived equivalence. We study transformations of Brauer complexes which preserve class of derived equivalence. Additionally, we establish ...

We show how any finite-dimensional algebra can be realized as an idempotent subquotient of some symmetric quasihereditary algebra. In the special case of rigid symmetric algebras, we show that they can be realized as centralizer subalgebras of symmetric quasi-hereditary algebras. We also show that the infinite-dimensional symmetric quasi-hereditary algebras we construct admit quasi-hereditary s...

In this paper, some left-symmetric algebras are constructed from linear functions. They include a kind of simple left-symmetric algebras and some examples appearing in mathematical physics. Their complete classification is also given, which shows that they can be regarded as generalization of certain 2-dimensional left-symmetric algebras.

Abstract. We show how any finite-dimensional algebra can be realized as an idempotent subquotient of some symmetric quasihereditary algebra. In the special case of rigid symmetric algebras we show that they can be realized as centralizer subalgebras of symmetric quasi-hereditary algebras. We also show that the infinite-dimensional symmetric quasi-hereditary algebras we construct admit quasi-her...