scholarly journals Free-Algebra Functors from a Coalgebraic Perspective

2020 ◽  
pp. 55-67
Author(s):  
H. Peter Gumm
Keyword(s):  
Free Algebra

Finitely generated free Heyting algebras

1986 ◽  
Vol 51 (1) ◽  
pp. 152-165 ◽  
Author(s):  
Fabio Bellissima
Keyword(s):  
Free Algebra ◽  
Kripke Semantics ◽  
Heyting Algebras ◽  
Free Algebras ◽  
Finitely Generated ◽  
Algebraic Properties

AbstractThe aim of this paper is to give, using the Kripke semantics for intuitionism, a representation of finitely generated free Heyting algebras. By means of the representation we determine in a constructive way some set of “special elements” of such algebras. Furthermore, we show that many algebraic properties which are satisfied by the free algebra on one generator are not satisfied by free algebras on more than one generator.

scholarly journals Probabilist Set Inversion using Pseudo-Intervals Arithmetic

2014 ◽  
Vol 15 (1) ◽  
pp. 097
Author(s):  
Abdelouahab KENOUFI
Keyword(s):  
Vector Space ◽  
Free Algebra ◽  
Interval Arithmetic ◽  
Semi Group ◽  
Numerical Examples ◽  
Inclusion Function ◽  
Python Programming

<pre><!--StartFragment-->In this paper, we present how to use an interval arithmetic framework based on free algebra construction, in order to build better defined inclusion function for interval semi-group and for its associated vector space. One introduces the <span>psi</span>-algorithm, which performs set inversion of functions and exhibits some numerical examples developed with the python programming langage<!--EndFragment--></pre>.

scholarly journals Supersymmetric gauge theories with a free algebra of invariants

1998 ◽  
Vol 531 (1-3) ◽  
pp. 507-524 ◽  
Author(s):  
Gustavo Dotti ◽  
Aneesh V. Manohar ◽  
Witold Skiba
Keyword(s):  
Free Algebra ◽  
Gauge Theories ◽  
Supersymmetric Gauge Theories ◽  
Supersymmetric Gauge

Finite Projective Distributive Lattices

1970 ◽  
Vol 13 (1) ◽  
pp. 139-140 ◽  
Author(s):  
G. Grätzer ◽  
B. Wolk
Keyword(s):  
Distributive Lattice ◽  
Free Algebra ◽  
Distributive Lattices ◽  
Free Algebras ◽  
Algebra Ii

The theorem stated below is due to R. Balbes. The present proof is direct; it uses only the following two well-known facts: (i) Let K be a category of algebras, and let free algebras exist in K; then an algebra is projective if and only if it is a retract of a free algebra, (ii) Let F be a free distributive lattice with basis {xi | i ∊ I}; then ∧(xi | i ∊ J0) ≤ ∨(xi | i ∊ J1) implies J0∩J1≠ϕ. Note that (ii) implies (iii): If for J0 ⊆ I, a, b ∊ F, ∧(xi | i ∊ J0)≤a ∨ b, then ∧ (xi | i ∊ J0)≤ a or b.

l′-Isolated Maps and Localizations

1983 ◽  
Vol 35 (2) ◽  
pp. 193-217
Author(s):  
Sara Hurvitz
Keyword(s):  
Finite Number ◽  
Free Algebra ◽  
Nilpotent Groups ◽  
Homotopy Groups ◽  
Homology Groups ◽  
Rational Cohomology ◽  
Locally Nilpotent Groups ◽  
Definition Of ◽  
Simply Connected ◽  
Path Connected

Let P be the set of primes, l ⊆ P a subset and l′ = P – l Recall that an H0-space is a space the rational cohomology of which is a free algebra.Cassidy and Hilton defined and investigated l′-isolated homomorphisms between locally nilpotent groups. Zabrodsky [8] showed that if X and Y are simply connected H0-spaces either with a finite number of homotopy groups or with a finite number of homology groups, then every rational equivalence f : X → Y can be decomposed into an l-equivalence and an l′-equivalence.In this paper we define and investigate l′-isolated maps between pointed spaces, which are of the homotopy type of path-connected nilpotent CW-complexes. Our definition of an l′-isolated map is analogous to the definition of an l′-isolated homomorphism. As every homomorphism can be decomposed into an l-isomorphism and an l′-isolated homomorphism, every map can be decomposed into an l-equivalence and an l′-isolated map.

scholarly journals Bounded endomorphisms of free P-algebras

1992 ◽  
Vol 34 (2) ◽  
pp. 209-214
Author(s):  
Daniel Ševčovič
Keyword(s):  
Free Algebra ◽  
Present Note ◽  
Finitely Generated ◽  
Efficient Tool ◽  
Pseudocomplemented Lattices

The present note deals with bounded endomorphisms of free p-algebras (pseudocomplemented lattices). The idea of bounded homomorphisms was introduced by R. McKenzie in [8]. T. Katriňák [5] subsequently studied the properties of bounded homomorphisms for the varieties of p-algebras. This concept is also an efficient tool for the characterization of, so-called, splitting as well as projective algebras in the varieties of all lattices or p-algebras. For details the reader is referred to [2], [5], [6], [7] and other references therein. Let us emphasize that the main results that are contained in the above mentioned references strongly depend on the boundedness of each endomorphism of any finitely generated free algebra in a given variety.

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