In 1939, Gelfand and Kolmogorov published a paper [4], where they showed that for a (compact Hausdorff) topological space X, homomorphisms of the algebra of continuous functions C(X) to numbers are in a one-to-one correspondence with points of X. Paper [4] is famous for giving birth to the theory of normed rings. However, it is worth stressing that the Gelfand–Kolmogorov theorem may be viewed a...

Using fixed point method, we prove some new stability results for Lie $(alpha,beta,gamma)$-derivations and Lie $C^{ast}$-algebra homomorphisms on Lie $C^{ast}$-algebras associated with the Euler-Lagrange type additive functional equation begin{align*} sum^{n}_{j=1}f{bigg(-r_{j}x_{j}+sum_{1leq i leq n, ineq j}r_{i}x_{i}bigg)}+2sum^{n}_{i=1}r_{i}f(x_{i})=nf{bigg(sum^{n}_{i=1}r_{i}x_{i}bigg)} end{...

We study the vector-valued spectrum $\mathcal {M}_{u,\infty }(B_{\ell _2},B_{\ell _2})$, which is set of non-zero algebra homomorphisms from {A}_u(B_{\ell _2})$ (the uniformly continuous holomorphic functions on $B_{\ell _2}$) to

1 The Basics 3 1.1 Graphs and Digraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Graph Homomorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 The H-colouring Problem and Variants . . . . . . . . . . . . . . . . . . . . . 8 1.4 Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Polymorphisms . . . . . ....

Many recursive functions can be defined elegantly as the unique homomorphisms, between two algebras, two coalgebras, or one each, that are induced by some universal property of a distinguished structure. Besides the well-known applications in recursive functional programming, several basic modes of reasoning about scientific models have been demonstrated to admit such an exact meta-theory. Here...

The Goulden–Jackson cluster method is a powerful tool for counting words by occurrences of prescribed subwords, and was adapted Elizalde Noy permutations consecutive patterns. In this paper, we lift the to Malvenuto–Reutenauer algebra. Upon applying standard homomorphisms, our result specializes both as well q-analogue which keeps track inversion number statistic. We construct additional homomo...

States of unital Abelian lattice-groups (normalised positive group homomorphisms to R) provide an abstraction expected-value operators. A well-known theorem due Mundici asserts that the category (with unit-preserving lattice-group as morphisms) is equivalent algebraic MV-algebras, and their homomorphisms. Through this equivalence, states correspond certain [0,1]-valued functionals on which are ...