A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...

By recent results of M. Stronkowski, it is known that not all modes embed as subreducts into semimodules over commutative unital semirings. Related to this problem is the problem of constructing a (commutative unital) semiring defining the variety of semimodules whose idempotent subreducts lie in a given variety of modes. We provide a general construction of such semirings, along with basic exa...

Identity transformations, used as skip-connections in residual networks, directly connect convolutional layers close to the input and those close to the output in deep neural networks, improving information flow and thus easing the training. In this paper, we introduce two alternative linear transforms, orthogonal transformation and idempotent transformation. According to the definition and pro...

We investigate the extension of modal logics by bisimulation quantifiers and present a class of modal logics which is decidable when augmented with bisimulation quantifiers. These logics are refered to as the idempotent transduction logics and are defined using the programs of propositional dynamic logic including converse and tests. This is a nontrivial extension of the decidability of the pos...