Synonymer & Anagram | Engelska ordet UNITAL

Exempel på hur man kan använda UNITAL i en mening

• Only for unital algebras is there a stronger notion, of unital subalgebra, for which it is also required that the unit of the subalgebra be the unit of the bigger algebra.
• In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished subspace.
• Maximal ideals are important because the quotients of rings by maximal ideals are simple rings, and in the special case of unital commutative rings they are also fields.
• In mathematics, hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers.
• Authors who do not require rings to be unital omit condition 4 in the definition above; they would call the structures defined above "unital left R-modules".
• In the unital commutative case, for the C*-algebra C(X) of continuous functions on some compact X, Riesz–Markov–Kakutani representation theorem says that the positive functionals of norm ≤ 1 are precisely the Borel positive measures on X with total mass ≤ 1.
• In mathematics, coalgebras or cogebras are structures that are dual (in the category-theoretic sense of reversing arrows) to unital associative algebras.
• In mathematics, a bialgebra over a field K is a vector space over K which is both a unital associative algebra and a counital coassociative coalgebra.
• In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antihomomorphism satisfying a certain property.
• These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and bicrossproduct quantum groups.
• By the Gelfand–Naimark theorem, the category of localizable measurable spaces (with measurable maps) is equivalent to the category of commutative Von Neumann algebras (with normal unital homomorphisms of *-algebras).
• Specifically, it shows that if M is a unital, self-adjoint operator algebra in the C*-algebra B(H), for some Hilbert space H, then the weak closure, strong closure and bicommutant of M are equal.
• A unital quantale may be defined equivalently as a monoid in the category Sup of complete join-semilattices.
• For an infinite field k, a finite-dimensional, unital, associative k-algebra is a Frobenius algebra if it has only finitely many minimal right ideals.
• If R is a finite-dimensional unital algebra and M a finitely generated R-module then the socle consists precisely of the elements annihilated by the Jacobson radical of R.
• A monoid object in the category of complete join-semilattices Sup (with the monoidal structure induced by the Cartesian product) is a unital quantale.
• Each of the ±1 eigenspaces has the structure of a unital complex Jordan algebra explicitly arising as the complexification of a Euclidean Jordan algebra.
• In other words, it is a 8-dimensional unital non-associative algebra A over F with a non-degenerate quadratic form N (called the norm form) such that.
• These maps have to satisfy associativity and unitality conditions up to homotopy, much in the same way as the multiplication of a ring is associative and unital.
• In mathematics, Hurwitz's theorem is a theorem of Adolf Hurwitz (1859–1919), published posthumously in 1923, solving the Hurwitz problem for finite-dimensional unital real non-associative algebras endowed with a nondegenerate positive-definite quadratic form.

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