We investigate the relative cohomology and relative homology theories of $F$-Gorenstein modules, consider the relations between classical and $F$-Gorenstein (co)homology theories.

In this errata, we reconsider and modify two propositions and their corollaries which were written on epi-retractable and co-epi-retractable modules.

We generalize various properties of Yetter-Drinfeld modules over Hopf algebras to quasi-Hopf algebras. The dual of a finite dimensional Yetter-Drinfeld module is again a Yetter-Drinfeld module. The algebra H 0 in the category of Yetter-Drinfeld modules that can be obtained by modifying the multiplication in a proper way is quantum commutative. We give a Structure Theorem for Hopf modules in the...

Several modular multiplication algorithms have been reviewed. One modified modulo multiplication algorithm is chosen to be designed in simple hardware components. The proposed design is shown in blocks of the basic modules and the connections required between the basic components are shown in some details.

In recent work we called a ring R a GGCD ring if the semigroup of finitely generated faithful multiplication ideals of R is closed under intersection. In this paper we introduce the concept of generalized GCD modules. An R-moduleM is a GGCD module if M is multiplication and the set of finitely generated faithful multiplication submodules of M is closed under intersection. We show that a ring R ...

We propose a construction of anyon systems associated to quantum tori with real multiplication and the embedding of quantum tori in AF algebras. These systems generalize the Fibonacci anyons, with weaker categorical properties, and are obtained from the basic modules and the real multiplication structure.

We present novel algorithms to factor polynomials over a finite field Fq of odd characteristic using rank 2 Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomial f(x) ∈ Fq[x] to be factored) with respect to a Drinfeld module φ with complex multiplication. Factors of f(x) supported on prime ideals with supersingular reducti...