ISSN:
1572-9095
Keywords:
left linear theory
;
barycentric theory
;
convexity theory
;
module theory
;
tensor product
;
inner hom
;
Primary 08C99
;
Secondary 16D10
;
18C05
;
18D15
;
52A01
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper we introduce left linear theories of exponentN (a set) on the setL as mapsL ×L N ∋ (l, λ) →l · λ ∈L such that for alll ∈L and λ, μ ∈L N the relation (l · λ)μ =l(λ · μ) holds, where λ · μ ∈L N is given by (λ · μ)(i) = λ(i)μ,i ∈N. We assume thatL has a unit, that is an element δ ∈L N withl · δ =l, for alll ∈L, and δ · λ = λ, for all λ ∈L N . Next, left (resp. right)L-modules andL-M-bimodules and their homomorphisms are defined and lead to categoriesL-Mod, Mod-L, andL-M-Mod. These categories are algebraic categories and their free objects are described explicitly. Finally, Hom(X, Y) andX ⊗Y are introduced and their properties are investigated.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00873297
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