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An algebra of product families
2009
Journal of Software and Systems Modeling
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Our approach is illustrated with a Haskell prototype implementation of one particular model of product family algebra. ...
We use the well established mathematical structure of idempotent semirings as the basis for a product family algebra that allows a formal treatment of the above notions. ...
of an automated theorem prover in the context of product family algebra. ...
doi:10.1007/s10270-009-0127-2
fatcat:xyfxwwiklfahzbrdjfy2477nou
A Tool for Formal Feature Modeling Based on BDDs and Product Families Algebra
2010
Workshop em Engenharia de Requisitos
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We propose a tool based on Product Families Algebra (PFA) and on Binary Decision Diagrams (BDD). ...
Feature models are commonly used to capture the commonality and the variability of product families. ...
A collection of products (an element of P(IP)) is called product family. ...
dblp:conf/wer/AlturkiK10
fatcat:62ynpjrlungzjed3qmh5vgeywe
An Aspect-Oriented Language for Product Family Specification
2012
Procedia Computer Science
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Based on the specification language of PFA (Product Family Algebra), we present a language AO-PFA (Aspect-Oriented Product Family Algebra) that extends the aspect-oriented paradigm to feature modeling. ...
This paper proposes an aspect-oriented approach at the feature-modeling level to better handle crosscutting concerns in the modeling of product families of ambient systems. ...
Each product family is defined as an equation with a product families label at the left side and a product family algebra term at the right side. ...
doi:10.1016/j.procs.2012.06.062
fatcat:4vnpzjm35nesfc7taichwwdm7y
Algebraic View Reconciliation
2008
2008 Sixth IEEE International Conference on Software Engineering and Formal Methods
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This paper proposes an algebraic solution. It uses sets of integration constraints that link (families of) system features in one view to other (families of) features in the same or a different view. ...
Both, families and constraints, are formalised using a feature algebra. ...
Definition 2.2 A feature algebra is an idempotent and commutative semiring. Its elements are called product families. ...
doi:10.1109/sefm.2008.36
dblp:conf/sefm/HofnerKM08
fatcat:rlndklunajayxlon6hlznpwzue
On the Directly and Subdirectly Irreducible Many-Sorted Algebras
2015
Demonstratio Mathematica
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AbstractA theorem of single-sorted universal algebra asserts that every finite algebra can be represented as a product of a finite family of finite directly irreducible algebras. ...
Moreover, we show that the theorem of Birkhoff, according to which every single-sorted algebra is isomorphic to a subdirect product of subdirectly irreducible algebras, is also true in the field of many-sorted ...
finite many-sorted algebra can also be represented as a product of a finite family of finite directly irreducible manysorted algebras. ...
doi:10.1515/dema-2015-0001
fatcat:gd7rguxeujhubeiquoa6i6a5ke
Page 604 of Mathematical Reviews Vol. 39, Issue 3
[page]
1970
Mathematical Reviews
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This defines an equivalence relation on the class of such families, families sharing the same tensor product being equivalent. ...
By means of an ingenious
| construction in C° the author produces a set S, an algebra
| A of functions on S such that ®,=S, and a related algebra
| B. ...
The Countable Chain Condition for C*-Algebras
[article]
2014
arXiv
pre-print
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We show independence from ZFC of the statement that this condition is preserved under the tensor products of C*-algebras. ...
In this paper, we introduce the countable chain condition for C*-algebras and study its fundamental properties. ...
The minimal tensor product of a family of unital CCC C*-algebras has CCC if for every finite subfamily, its minimal tensor product has CCC. Theorem 1.2. ...
arXiv:1405.1100v1
fatcat:t74kp5mfengkxbbgnkhmt6kesy
Cup product on A_∞-cohomology and deformations
[article]
2021
arXiv
pre-print
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As an example, we construct a minimal A_∞-algebra from the Weyl-Moyal ∗-product algebra of polynomial functions. ...
We propose a simple method for constructing formal deformations of differential graded algebras in the category of minimal A_∞-algebras. ...
In order to make the DGA A t into a family of A ∞ -algebras, we define the tensor product algebra A t ⊗ k[[u]], where u is an auxiliary formal variable of degree 2. ...
arXiv:1901.07872v3
fatcat:6skel4zn75a7xmxwvzzsif6aum
On some structural properties of evolution algebras
[article]
2023
arXiv
pre-print
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2023 pre-print arXiv:2311.00102v1 fatcat:zqflzy77qvgqdlqzkuxxd22qpy
We consider the intersection 𝔐(A) of all maximal ideals of an evolution algebra A and study the structure of the quotient A/(A). ...
We investigate the superfluous members both in the family of maximal ideals and also in the set of hereditary subsets of the associated graphs. ...
As an immediate consequence of the definition of subdirect product, if {I α } α∈Λ is a family of ideals of A and S := ∩ α I α then A/S ∼ = α∈Λ s A/I α . ...
arXiv:2311.00102v2
fatcat:udmky3js6jhbvh7btvh7r6fv4m
Certain free products of graph operator algebras
[article]
2008
arXiv
pre-print
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Using the free product description of these algebras we investigate the K-theory of these algebras. ...
These algebras arise as free products of directed graph algebras with amalgamation. We then determine the C^*-envelopes for a large class of the non-selfadjoint algebras. ...
Notice that if V (G) = 1 and f (e) = f (g) implies e = g, then the algebra A(G, f ) is an example of the semicrossed products for multivariable dynamics of [4] , whose free product description motivated ...
arXiv:0809.0848v1
fatcat:2nccmknq6bfcnjcdqqrii7exhy
A class of unbounded operator algebras, IV
1978
Journal of Mathematical Analysis and Applications
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TENSOR PRODUCTS OF UNBOUNDED HILBERT ALGEBRAS Let Qr (resp. g2) be an unbounded Hilbert algebra over (2@r),, (resp. (B&J. Let .C?i @ ga be the algebraic tensor product of gr and ga . ...
An EW#-algebra 2l is called weakly unbounded if there exists a family {21z,},,, of von Neumann algebras 211, such that g is a *-subalgebra of nAEn 21A and K = enEn 21c, . ...
doi:10.1016/0022-247x(78)90041-0
fatcat:dxkjhps2kzg4lhaemqwm3ohco4
Finiteness of semigroups of operators in universal algebra
1967
Canadian Journal of Mathematics - Journal Canadien de Mathematiques
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A universal algebra U is a subdirect product of the family (A t ) iei of universal algebras if it is a subalgebra of the direct product Yl^ t (i £ -0 an d if, for each i, the restriction to U of the natural ...
The quotient algebra Yl^ */3 °f Yl^ t modulo this congruence relation is called a filter product of the family (Ai) iei . If 5 is an ultrafilter, IJ^U/S * s called an ultraproduct; see (1) . ...
doi:10.4153/cjm-1967-070-8
fatcat:u5aimuyy2bcr3owrgyrk2okg6i
Certain free products of graph operator algebras
2010
Journal of Mathematical Analysis and Applications
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We associate to these generalized Cuntz-Krieger families a directed graph, with a coloring function on the edge set. We call such a directed graph an edge-colored directed graph. ...
Using the free product description of these algebras we investigate the K -theory of these algebras. The operator algebras of directed graphs are important for two reasons. ...
A further consequence of this free product construction is the following result which applies to graph algebras and hence allows graph algebras to be written as free products of simpler algebras. ...
doi:10.1016/j.jmaa.2009.11.023
fatcat:kbd2gqhhdjep3hi2sthfp5xjwq
Generalized free products of boolean algebras with an amalgamated subalgebra
1963
Indagationes Mathematicae (Proceedings)
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The definition of the generalized free product of a family of Boolean algebras with an amalgamated subalgebra will be given in a way which is analogous to the definition of free products (cf. [6] ). ...
The generalized free product of a family of Boolean algebras with an amalgamated subalgebra exists and is unique (up to jsomorphisms). Proof. We use the notation of section 1. ...
doi:10.1016/s1385-7258(63)50024-9
fatcat:ff6n46sq7nht7ixy4m5zwcn5ty
Algebra objects and algebra families for finite limit theories
1992
Journal of Pure and Applied Algebra
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An afgebra family for T in %' is an (ordinary) algebra for T in Fam % and a co-algebra family for T in (e is a T-algebra in Fam (cop. ...
The free product completion of % is the category (Fam %Op)Op and a representing object is then a family of objects of %. ...
We have also had the benefit of helpful advice from an anonymous referee. The work was supported financially by the ARC.
References ...
doi:10.1016/0022-4049(92)90047-j
fatcat:bxe6koxmezhirhcfw4u3rx3igm
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