On path space kQ, there is a trivial kQ-module structure determined by the multiplication of path algebra kQ and a trivial kQ-comodule structure determined by the comultiplication of path coalgebra kQ. In this paper, on path space kQ, a nontrivial kQ-module structure is defined, and it is proved that this nontrivial left kQ-module structure is isomorphic to the dual module structure of trivial ...

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...

Let $R\ $be a commutative ring with $1\neq0$ and $M$ be an $R$-module. Suppose that $S\subseteq R\ $is multiplicatively closed set of $R.\ $Recently Sevim et al. in \cite{SenArTeKo} introduced the notion $S$-prime submodule which is generalization prime used them to characterize certain classes rings/modules such as submodules, simple modules, torsion free modules,\ $S$-Noetherian modules etc. ...

We present a novel randomized algorithm 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 ∈ Fq[x] to be factored) with respect to a random Drinfeld module φ with complex multiplication. Factors of f supported on prime ideals with supersin...

The paper presents the concepts behind the "Urdhva Tiryagbhyam Sutra" and "Nikhilam Sutra" multiplication techniques. It then shows the architecture for a 16×16 Vedic multiplier module using Urdhva Tiryagbhyam Sutra. The paper then extends multiplication to 16×16 Vedic multiplier using "Nikhilam Sutra" technique. The 16×16 Vedic multiplier module using Urdhva Tiryagbhyam Sutra uses four 8×8 Ved...

The thermal safety of lithium-ion traction batteries is a highly concerning issue in the field electric transportation. large amount gas emissions during runaway process has high hazards, such as fire and explosion. quantitative analysis one important challenges testing evaluating battery safety. Focusing on quantifying using large-scale propagation modules packs, based idea cell result multipl...

Bit-sequential multiplier is being studied in a (+1, -1) binary representation. The maximum length of multiplier for a fix point numbers consists of n module. Each module is a five bit adder which contains 5 inputs and 3 outputs. It also contains an additional pin at the input as well as at the output. Computation time for multiplication is of the order of O(n). Hardware realization of module i...

Let H(S) be the Hardy space on the unit sphere S in C, n ≥ 2. Then H(S) is a natural Hilbert module over the ball algebra A(B). Let Mz1 , ..., Mzn be the module operators corresponding to the multiplication by the coordinated functions. Each submodule M ⊂ H(S) gives rise to the module operators ZM,j = Mzj |M, j = 1, ..., n, on M. In this paper we establish the following commonly believed, but n...

We define evaluation forms associated to objects in a module subcategory of Ext-symmetry generated by finitely many simple modules over a path algebra with relations and prove a multiplication formula for the product of two evaluation forms. It is analogous to a multiplication formula for the product of two evaluation forms associated to modules over a preprojective algebra given by Geiss, Lecl...