Structure of Locally Idempotent Algebras
نویسنده
چکیده
It is shown that every locally idempotent (locallym-pseudoconvex) Hausdorff algebra A with pseudoconvex vonNeumannbornology is a regular (respectively, bornological) inductive limit of metrizable locallym-(kB-convex) subalgebras AB of A. In the case where A, in addition, is sequentially BA-complete (sequentially advertibly complete), then every subalgebraAB is a locally m-(kB-convex) Fréchet algebra (respectively, an advertibly complete metrizable locally m-(kB-convex) algebra) for some kB ∈ (0, 1]. Moreover, for a commutative unital locally m-pseudoconvex Hausdorff algebra A over C with pseudoconvex von Neumann bornology, which at the same time is sequentially BA-complete and advertibly complete, the statements (a)–(j) of Proposition 3.2 are equivalent.
منابع مشابه
Product preservation and stable units for reflections into idempotent subvarieties
We give a necessary and sufficient condition for the preservation of finite products by a reflection of a variety of universal algebras into an idempotent subvariety. It is also shown that simple and semi-left-exact reflections into subvarieties of universal algebras are the same. It then follows that a reflection of a variety of universal algebras into an idempotent subvariety has stable units...
متن کاملRepresentations of Topological Algebras by Projective Limits
It is shown that a) it is possible to define the topology of any topological algebra by a collection of F -seminorms, b) every complete locally uniformly absorbent (complete locally A-pseudoconvex) Hausdorff algebra is topologically isomorphic to a projective limit of metrizable locally uniformly absorbent algebras (respectively, A-(k-normed) algebras, where k ∈ (0, 1] varies, c) every complete...
متن کاملRepresentable Idempotent Commutative Residuated Lattices
It is proved that the variety of representable idempotent commutative residuated lattices is locally finite. The n-generated subdirectly irreducible algebras in this variety are shown to have at most 3n+1 elements each. A constructive characterization of the subdirectly irreducible algebras is provided, with some applications. The main result implies that every finitely based extension of posit...
متن کاملSTONE DUALITY FOR R0-ALGEBRAS WITH INTERNAL STATES
$Rsb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras and the category of t...
متن کاملRealization of locally extended affine Lie algebras of type $A_1$
Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...
متن کامل