We assign a relational structure to any finite algebra in canonical way, using solution sets of equations, and we prove that this is polymorphism-homogeneous if only the itself polymorphism-homogeneous. show polymorphism-homogeneity also equivalent property algebraic (i.e., systems equations) are exactly those tuples closed under centralizer clone algebra. Furthermore, aforementioned properties...

Isbell and Semadeni [Trans. Amer. Math. Soc. 107 (1963)] proved that every infinite-dimensional $1$-injective Banach space contains a hyperplane is $(2+\varepsilon )$-injective for $\varepsilon \gt 0$, yet not $2$-injective, rem

LetR be a ring andM a rightR-module with S= End(MR). The moduleM is called almost principally quasi-injective (or APQ-injective for short) if, for any m∈M, there exists an S-submodule Xm of M such that lMrR(m) = Sm ⊕ Xm. The module M is called almost quasiprincipally injective (or AQP-injective for short) if, for any s∈ S, there exists a left ideal Xs of S such that lS(ker(s)) = Ss ⊕ Xs. In thi...

Denef and Loeser defined a map from the Grothendieck ring of sets definable in pseudo-finite fields to the Grothendieck ring of Chow motives, thus enabling to apply any cohomological invariant to these sets. We generalize this to perfect, pseudo algebraically closed fields with pro-cyclic Galois group. In addition, we define some maps between different Grothendieck rings of definable sets which...

The unit quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Often, quaternion-based feedback control laws require an additional mechanism that lifts a continuous attitude trajectory to the unit quaternion space. Lifting mechanisms that are memoryless, for example, selecting the quaternion having positive scalar component, h...

In our recent work we gave a treatment of certain aspects of multiplication modules, projective modules, flat modules and cancellation-like modules via idealization. The purpose of this work is to continue our study and develop the tool of idealization, particularly in the context of closed, divisible injective, and simple modules. We determine when a ring R (M), the idealization of M , is a qu...

We show that the Green correspondence induces an injective group homomorphism from linear source Picard L(B) of a block B finite algebra to L(C), where C is Brauer correspondent B. This maps trivial T(B) T(C). further endopermutation E(B) bounded in terms defect groups and when has normal E(B)=L(B). Finally we prove rank any invertible B-bimodule by

Abstract Let k be an algebraically closed field of characteristic p > 0 and let G a symplectic or general linear group over . We consider induced modules for under the assumption that is bigger than greatest hook length in partitions involved. give explicit constructions left resolutions by tilting modules. Furthermore, we injective certain truncated categories. show multiplicities indecompo...