**isomorphism** in English

identity or similarity of form or appearance (Biology)

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**"isomorphism"**from the English Dictionary. We can refer to these sentence patterns for sentences in case of finding sample sentences with the word "isomorphism", or refer to the context using the word "isomorphism" in the English Dictionary.

1. In particular, there are uncountably many **isomorphism** classes of UHF C*-algebras.

2. Determining whether two graphs are isomorphic is referred to as the graph **isomorphism** problem.

3. If an **isomorphism** exists between two graphs, then the graphs are called isomorphic.

4. In algebraic geometry, this classification of (**isomorphism** classes of) complex line bundles by the first Chern class is a crude approximation to the classification of (**isomorphism** classes of) holomorphic line bundles by linear equivalence classes of divisors.

5. For example, many concepts in category theory are defined to be unique up to **isomorphism**.

6. As we have seen, up to **isomorphism**, there are four groups, two abelian, and two non-abelian.

7. Other instances of the **isomorphism** of thallous with potassium salts are the nitrates, phosphates, hydrazoates, sulphates, chromates, selenates, and the Analogously …

8. Together with Alessandro Berarducci, he demonstrated an **isomorphism** between the strictly-positive algebraic data types and the polymorphic lambda-terms, otherwise known as Böhm–Berarducci encoding.

9. An important role is played in the theory of rings and Algebras, as in any other algebraic theory, by the notions of homomorphism and **isomorphism**.

10. A countable periodic reduced abelian group is determined uniquely up to **isomorphism** by its Ulm invariants for all prime numbers p and countable ordinals α.

11. In fact, the parallel of f is an **isomorphism** for every morphism f if and only if the pre-abelian category is an abelian category.

12. In algebraic categories (specifically, categories of varieties in the sense of universal algebra), an **isomorphism** is the same as a homomorphism which is bijective on underlying sets.

13. In mathematics, the Satake **isomorphism**, introduced by Satake (1963), identifies the Hecke algebra of a reductive group over a local field with a ring of invariants of the Weyl group.

14. The Adjunction formula states that if $Y \\subset M$ is a smooth analytic hypersurface then we have an **isomorphism** $N^*_Y \\simeq [-Y]_Y$, where $N_Y$ is the normal

15. (Remember that “117·1” is really shorthand for 1+1+···+1 — 1 added to itself 117 times.) In fact, it is the only inﬁnite Cyclic group up to **isomorphism**

16. Lemma 11 (Kahrobaei [6]) Suppose [phi] : A [right arrow] B is an **isomorphism** between two groups A and B: Let C < A; and let D be the amalgamated product of A and B Amalgamating C with C[phi]:

17. Work focused on several specific problems, including ramified spectral covers, explicit examples of families of smooth curves having infinite monodromy for the Hitchin connection in rank 2, vector bundles in positive characteristic, and affine Lie algebras of the celebrated strange duality **isomorphism** between spaces of generalised theta functions.

18. The Classification of a collection of objects generally means that a list has been constructed with exactly one member from each **isomorphism** type among the objects, and that tools and techniques can effectively be used to identify any combinatorially given object with its unique representative in the list