Let $f : A rightarrow B$ be a ring homomorphism and $J$ an ideal of $B$. In this paper, we give a necessary and sufficient condition for the amalgamated algebra along an ideal $Abowtie^fJ$ to be $J$-Noetherian. Then we give a characterization for pseudo-irreducible ideals of $Abowtie^fJ$, in special cases.

We present an investigation of duality in the traditional logical manner. We extend Nelson's symmetrization of intuitionistic logic, constructible falsity, to a self-dual logic; constructible duality. We develop a self-dual model by considering an interval of worlds in an intuitionistic Kripke model. The duality arises through how we judge truth and falsity. Truth is judged forward in the Kripk...

BCK-algebras, introduced in the 1960s by Imai and Iséki [3], form a well-known class of algebras intensively studied in algebraic logic during the last decades. The reason of their introduction was practically twofold: they describe general properties of algebras of sets with the set subtraction as a binary operation, and secondly, they form a natural generalization of algebraic counterparts of...

This paper analyzes the action δ of a Lie algebra X by derivations on a C*–algebra A. This action satisfies an “almost inner” property which ensures affiliation of the generators of the derivations δ with A, and is expressed in terms of corresponding pseudo–resolvents. In particular, for an abelian Lie algebra X acting on a primitive C*–algebra A, it is shown that there is a central extension o...

if we formulate our logics in a Gentzen-type formal system. Some syntactical properties of these logics have been studied firstly by the second author in [I I], in connection with the study of BCK-algebras (for information on BCK-algebras, see [9]). There, it turned out that such a syntactical method is a powerful and promising tool in studying BCK-algebras. Using this method, considerable prog...

In this paper we use continuous family of multisections of the moduli space of pseudo holomorphic discs to partially improve the construction of Lagrangian Floer cohomology of [13] in the case of R coefficient. Namely we associate cyclically symmetric filtered A∞ algebra to every relatively spin Lagrangian submanifold. We use the same trick to construct a local rigid analytic family of filtered...