There exists Clause Samples

There exists a deterministic polynomial-time algorithm that, given a finite ring R and a finite R-module M, determines whether M is simple or not.
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There exists a deterministic polynomial-time algorithm that, given a finite ring A, computes the generalised prime subring of A. 6.2 Separability‌
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There exists. > ( ) 1. Rf , Rg R1, > ( ) 2. Mf K1 Rf and = − i i ∈ + 3. Mg K1 Rg , such that we have the following. Firstly, for i 1, . . . , n 1 we can choose f , g E such that Log(fi) ∈ B(li(Mf ), R) and Log(gi) ∈ B(li(Mg), R). Furthermore, after writing Vf = ⟨f1, . . . fn−1⟩ and Vg = ⟨g1, . . . gn−1⟩ i ∈ + f = ⟨ 1 n−1⟩ [ ∶ ] [ ∶ ] we have that E+ Vf is coprime to E+ Vg .
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Related to There exists

  • Corporate Existence, Etc Subject to Section 10.2, the Company will at all times preserve and keep its corporate existence in full force and effect. Subject to Section 10.2, the Company will at all times preserve and keep in full force and effect the corporate existence of each of its Subsidiaries (unless merged into the Company or a Wholly-Owned Subsidiary) and all rights and franchises of the Company and its Subsidiaries unless, in the good faith judgment of the Company, the termination of or failure to preserve and keep in full force and effect such corporate existence, right or franchise would not, individually or in the aggregate, have a Material Adverse Effect.

  • Company Existence During the term of this Agreement, the Seller shall keep in full force and effect its existence, rights and franchises as a limited liability company under the laws of the jurisdiction of its formation and shall obtain and preserve its qualification to do business in each jurisdiction in which such qualification is or shall be necessary to protect the validity and enforceability of the Basic Documents and each other instrument or agreement necessary or appropriate to the proper administration of this Agreement and the transactions contemplated hereby. In addition, all transactions and dealings between the Seller and its Affiliates (including the Issuer) shall be conducted on an arm’s length basis.

  • Corporate Existence So long as the Buyer beneficially owns any Note, the Company shall maintain its corporate existence and shall not sell all or substantially all of the Company’s assets, except in the event of a merger or consolidation or sale of all or substantially all of the Company’s assets, where the surviving or successor entity in such transaction (i) assumes the Company’s obligations hereunder and under the agreements and instruments entered into in connection herewith and (ii) is a publicly traded corporation whose Common Stock is listed for trading on the OTCBB, Nasdaq, Nasdaq SmallCap, NYSE or AMEX.

  • Legal Existence Subject to Article Five hereof, the Company shall do or cause to be done all things necessary to preserve and keep in full force and effect (i) its legal existence, and the corporate, partnership or other existence of each Restricted Subsidiary, in accordance with the respective organizational documents (as the same may be amended from time to time) of each Restricted Subsidiary and the material rights (charter and statutory), licenses and franchises of the Company and its Restricted Subsidiaries; provided that the Company shall not be required to preserve any such right, license or franchise, or the corporate, partnership or other existence of any of its Restricted Subsidiaries if the Board of Directors of the Company shall determine that the preservation thereof is no longer desirable in the conduct of the business of the Company and its Restricted Subsidiaries taken as a whole, and that the loss thereof is not adverse in any material respect to the Holders.

  • Maintain Existence It will preserve and maintain its existence, rights, franchises and privileges in the jurisdiction of its formation, and qualify and remain qualified in good standing as a foreign trust or limited liability company in each jurisdiction where its business is conducted, and will obtain and maintain all requisite authority to conduct its business in each jurisdiction in which its business requires such authority.