An embedding theorem for partial algebras and the free completion of a free partial algebra within a primitive class

1973 ◽  
Vol 3 (1) ◽  
pp. 271-279 ◽  
Author(s):  
P. Burmeister
Keyword(s):  
Embedding Theorem ◽  
Partial Algebra ◽  
Partial Algebras

scholarly journals Unsolid and fluid strong varieties of partial algebras

2006 ◽  
Vol 2006 ◽  
pp. 1-19
Author(s):  
S. Busaman ◽  
K. Denecke
Keyword(s):  
Partial Algebra ◽  
The Other ◽  
Turing Machines ◽  
Left Hand ◽  
Recursive Functions ◽  
Right Hand ◽  
Algebraic Description ◽  
Partial Recursive Functions ◽  
Partial Algebras ◽  
The Right

A partial algebra𝒜=(A;(fiA)i∈I)consists of a setAand an indexed set(fiA)i∈Iof partial operationsfiA:Ani⊸→A. Partial operations occur in the algebraic description of partial recursive functions and Turing machines. A pair of termsp≈qover the partial algebra𝒜is said to be a strong identity in𝒜if the right-hand side is defined whenever the left-hand side is defined and vice versa, and both are equal. A strong identityp≈qis called a strong hyperidentity if when the operation symbols occurring inpandqare replaced by terms of the same arity, the identity which arises is satisfied as a strong identity. If every strong identity in a strong variety of partial algebras is satisfied as a strong hyperidentity, the strong variety is called solid. In this paper, we consider the other extreme, the case when the set of all strong identities of a strong variety of partial algebras is invariant only under the identical replacement of operation symbols by terms. This leads to the concepts of unsolid and fluid varieties and some generalizations.

scholarly journals NeutroAlgebra is a Generalization of Partial Algebra

2020 ◽  
pp. 08-17
Author(s):  
Florentin Smarandache ◽  
Keyword(s):  
Partial Algebra ◽  
The Other ◽  
Partial Operation ◽  
Whole Space ◽  
Partial Algebras ◽  
Concept Attribute

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to and , and one corresponding to neutral (indeterminate) (also denoted ) between the opposites}, which may or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra is an algebra which has at least one NeutroOperation or one NeutroAxiom (axiom that is true for some elements, indeterminate for other elements, and false for the other elements). A Partial Algebra is an algebra that has at least one Partial Operation, and all its Axioms are classical (i.e. axioms true for all elements). Through a theorem we prove that NeutroAlgebra is a generalization of Partial Algebra, and we give examples of NeutroAlgebras that are not Partial Algebras. We also introduce the NeutroFunction (and NeutroOperation).

scholarly journals TOPOLOGICAL PARTIAL *-ALGEBRAS: BASIC PROPERTIES AND EXAMPLES

1999 ◽  
Vol 11 (03) ◽  
pp. 267-302 ◽  
Author(s):  
J.-P. ANTOINE ◽  
F. BAGARELLO ◽  
C. TRAPANI
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Product Space ◽  
Function Spaces ◽  
Partial Algebra ◽  
Inner Product Space ◽  
Inner Product ◽  
Partial Algebras ◽  
Amalgam Spaces ◽  
Locally Convex

Let [Formula: see text] be a partial *-algebra endowed with a topology τ that makes it into a locally convex topological vector space [Formula: see text]. Then [Formula: see text] is called a topological partial *-algebra if it satisfies a number of conditions, which all amount to require that the topology τ fits with the multiplier structure of [Formula: see text]. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of potential topological partial *-algebras, either function spaces (lattices of Lp spaces on [0, 1] or on ℝ, amalgam spaces), or partial *-algebras of operators (operators on a partial inner product space, O*-algebras).

Representability of invariant positive sesquilinear forms on partial *-algebras

1990 ◽  
Vol 108 (2) ◽  
pp. 337-353 ◽  
Author(s):  
J.-P. Antoine ◽  
A. Inoue
Keyword(s):  
Partial Algebra ◽  
Sesquilinear Forms ◽  
Sesquilinear Form ◽  
Partial Algebras ◽  
The Relationship

AbstractWe consider invariant positive sesquilinear forms on a (partial) *-algebra A without unit. First we investigate the relationship between extendability and representability for such a form ø; in particular we discuss under which conditions the two concepts are equivalent. Then we introduce the notions of weak representability and strict unrepresentability, and we show that every fully invariant positive sesquilinear form on A × A is uniquely decomposed into a weakly representable part and a strictly unrepresentable part.

scholarly journals Embedding Theorems and Area Operators on Bergman Spaces with Doubling Measure

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Changbao Pang ◽  
Antti Perälä ◽  
Maofa Wang
Keyword(s):  
Borel Measure ◽  
Bergman Spaces ◽  
Embedding Theorem ◽  
Weighted Bergman Spaces ◽  
Embedding Theorems ◽  
Positive Borel Measure ◽  
Doubling Property ◽  
Area Operator ◽  
Special Cases ◽  
Upper Half Plane

AbstractWe establish an embedding theorem for the weighted Bergman spaces induced by a positive Borel measure $$d\omega (y)dx$$ d ω ( y ) d x with the doubling property $$\omega (0,2t)\le C\omega (0,t)$$ ω ( 0 , 2 t ) ≤ C ω ( 0 , t ) . The characterization is given in terms of Carleson squares on the upper half-plane. As special cases, our result covers the standard weights and logarithmic weights. As an application, we also establish the boundedness of the area operator.

scholarly journals THE MEANING OF BASIC CATEGORY THEORETICAL NOTIONS IN SOME CATEGORIES OF PARTIAL ALGEBRAS. II PRODUCTS AND COPRODUCTS

1992 ◽  
Vol 25 (4) ◽  
Author(s):  
Peter Burmeister ◽  
Boleslaw Wojdyło
Keyword(s):  
Basic Category ◽  
Partial Algebras

scholarly journals Interpretability over peano arithmetic

1999 ◽  
Vol 64 (4) ◽  
pp. 1407-1425
Author(s):  
Claes Strannegård
Keyword(s):  
Modal Logic ◽  
Completeness Theorem ◽  
Peano Arithmetic ◽  
Embedding Theorem ◽  
Compactness Theorem ◽  
Partial Answer ◽  
Recursively Enumerable ◽  
Recursively Enumerable Sets ◽  
Interpretability Logic

AbstractWe investigate the modal logic of interpretability over Peano arithmetic. Our main result is a compactness theorem that extends the arithmetical completeness theorem for the interpretability logic ILMω. This extension concerns recursively enumerable sets of formulas of interpretability logic (rather than single formulas). As corollaries we obtain a uniform arithmetical completeness theorem for the interpretability logic ILM and a partial answer to a question of Orey from 1961. After some simplifications, we also obtain Shavrukov's embedding theorem for Magari algebras (a.k.a. diagonalizable algebras).

PUSHOUTS OF PARTIAL HOMOMORPHISMS OF PARTIAL ALGEBRAS II: CLOSED QUOMORPHISMS

2003 ◽  
Vol 02 (04) ◽  
pp. 471-500
Author(s):  
R. ALBERICH ◽  
F. ROSSELLÓ
Keyword(s):  
Basic Problem ◽  
Arbitrary Signature ◽  
Partial Algebras

We characterize the pairs of closed homomorphisms and closed quomorphisms of partial Σ-algebras that have a pushout in the corresponding category, for an arbitrary signature Σ. The latter characterization solves the basic problem previous to the development of a single-pushout approach to the transformation of partial algebras based on closed quomorphisms.

scholarly journals A note on a space Hp, a of holomorphic functions

1987 ◽  
Vol 35 (3) ◽  
pp. 471-479
Author(s):  
H. O. Kim ◽  
S. M. Kim ◽  
E. G. Kwon
Keyword(s):  
Hardy Space ◽  
Complex Plane ◽  
Unit Disc ◽  
Weak Type ◽  
Holomorphic Functions ◽  
Embedding Theorem ◽  
Type Operator ◽  
Taylor Coefficients ◽  
Bounded Holomorphic

For 0 < p < ∞ and 0 ≤a; ≤ 1, we define a space Hp, a of holomorphic functions on the unit disc of the complex plane, for which Hp, 0 = H∞, the space of all bounded holomorphic functions, and Hp, 1 = Hp, the usual Hardy space. We introduce a weak type operator whose boundedness extends the well-known Hardy-Littlewood embedding theorem to Hp, a, give some results on the Taylor coefficients of the functions of Hp, a and show by an example that the inner factor cannot be divisible in Hp, a.

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