Various embedding problems of lattices into complete lattices are solved. We prove that for any join-semilattice S with the minimal join-cover refinement property, the ideal lattice IdS of S is both algebraic and dually algebraic. Furthermore, if there are no infinite D-sequences in J(S), then IdS can be embedded into a direct product of finite lower bounded lattices. We also find a system of i...

The article reviews different definitions for a convolutional code which can be found in the literature. The algebraic differences between the definitions are worked out in detail. It is shown that bi-infinite support systems are dual to finite-support systems under Pontryagin duality. In this duality the dual of a controllable system is observable and vice versa. Uncontrollability can occur on...

By adding a linear term to a renormalization-group equation in a system exhibiting infinite-order phase transitions, the asymptotic behavior of running coupling constants is derived in an algebraic manner. A benefit of this method is presented explicitly using several examples.

The infinite braid group B∞ admits a left self-distributive structure. In particular, it includes a free monogenerated left self-distributive system, and, therefore, it inherits all properties of the latter object. Here we discuss how such algebraic properties translate into the language of braids. We state new results about braids and propose a list of open questions.