We show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. Hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. As aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. This generalizes and simplifies a result of  Dung and   Smith. As another consequen...

Although various dynamic or temporal logics have been proposed to verify quantum protocols and systems, these two viewpoints not studied comprehensively enough. We propose Linear Temporal Quantum Logic (LTQL), a linear extension of logic with implication, extend it Dynamic (DLTQL). This has operators express transitions by unitary (quantum gates) ones those projections (projective measurement)....

We classify the orbits of nets conics under action projective linear group and we determine specializations these orbits, using geometric algebraic methods. study related questions, as parametrization planar cubics. show that Artinian algebras Hilbert function $$ H=(1,3,3,0)$$ determined by nets, can be smoothed—deformed to a direct sum fields; $$H=(1,r,2,0)$$ , pencils quadrics, also smoothed....

We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms functions on projective Hilbert space, and its space analog, with a noncommutative product explicit coordinates discuss physical dynamical picture. The isomorphism is then used as base translation differential symplectic geometry infinite dimensional manifolds onto geometry. Hence, we obtain latt...

We derive a framework to apply topological quantum chemistry in systems subject magnetic flux. start by deriving the action of spatial symmetry operators uniform field, which extends Zak's translation groups all crystal groups. Ultimately, symmetries form projective representation group. As consequence, band representations acquire an extra gauge invariant phase compared non-magnetic theory. Th...

we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...