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...

Let H be a bialgebra and let A be an associative algebra. The algebra A is said to be an H-module-algebra if there is an H-module structure on A such that the multiplication on A becomes an H-module morphism. For example, if S denotes the Landweber-Novikov algebra [15, 21], then the complex cobordism MU(X) of a topological space X is an S module-algebra. Likewise, the singular mod p cohomology ...

Let R be a commutative ring with unity. And let E unitary R-module. This paper introduces the notion of 2-prime submodules as generalized concept ideal, where proper submodule H module F over is said to if , for r and x implies that or . we prove many properties this kind submodules, then only [N ] E, R. Also, non-zero multiplication module, [K: F] [H: every k such K. Furthermore, will study ba...

Let be a module over commutative ring with identity. Before studying the concept of Strongly Pseudo Nearly Semi-2-Absorbing submodule, we need to mention ideal and basics that you study submodule. Also, introduce several characteristics submodule in classes multiplication modules other types modules. We also had no luck because is not ideal. it noted under conditions, which this faithful module...

Let H be a bialgebra. An H-module-algebra is an associative algebra A that is also an H-module such that the multiplication map on A becomes an H-module morphism. This algebraic structure arises often in algebraic topology, quantum groups [11, Chapter V.6], Lie and Hopf algebras theory [3, 16, 19], and group representations [1, Chapter 3]. For example, in algebraic topology, the complex cobordi...

Let G be a finite group of complex n× n unitary matrices generated by reflections acting on C. Let R be the ring of invariant polynomials, and χ be a multiplicative character of G. Let Ω be the R-module of χ-invariant differential forms. We define a multiplication in Ω and show that under this multiplication Ω has an exterior algebra structure. We also show how to extend the results to vector f...

FPGAs are increasingly being used in the high performance and scientific computing community to implement floating-point based hardware accelerators. We present FPGA floating-point multiplication. Such circuits can be extremely useful in the FPGA implementation of complex systems that benefit from the reprogramability and parallelism of the FPGA device but also require a general purpose multipl...

Polynomial multiplication is the most computationally expensive part of lattice-based cryptography algorithm. However, existing acceleration schemes have problems, such as low performance and high hardware resource overhead. Based on polynomial number theoretic transformation (NTT), this paper proposed a simple element Montgomery module reduction with pipeline structure to realize fast multipli...

A calyx (multiplicative lattice) is a complete lattice endowed with the structure of a monoid such that multiplication by an element is a left adjoint functor of complete lattices (equivalently, a left adjoint functor which preserves colimits). Calyxes are a generalization of the set of ideals of a ring, which form a complete lattice under intersection and summation; in conjunction with the nat...