LLP, Limited Liability Partnership: a partnership where a partner's liability for the debts of the partnership is limited except in the case of liability for acts of professional negligence or malpractice. In some states, LLPs may only be formed for purposes of practicing a licensed profession, typically attorneys, accountants and architects. This is often the only form of limited partnership allowed for law firms (as opposed to general partnerships).
Nebraska corporation, incorporated, company, or limited, or the abbreviation corp., inc., co., or ltd., or words or abbreviations of like import in another language, except that a corporation organized to conduct a banking business under the Nebraska Banking Act may use a name which includes the word bank without using any such words or abbreviations Section 21-2028 State of Nebraska Statutes
Cooperative (aguda shitufit, אגודה שיתופית) – entity which may pursue profit, but with certain legal properties meant to facilitate greater participation by each shareholder, or member, in the entity's affairs. Shareholders usually have an additional relationship with the cooperative, such as employees or consumers. This type of entity is found mainly in agriculture (a kibbutz or moshav is often a cooperative), transportation, or certain types of marketing operations associated with agricultural products. Cooperatives are governed by the Cooperatives Ordinance (פקודת האגודות השיתופיות).
Corp., Inc., Corporation, Incorporated: used to denote corporations (public or otherwise). These are the only terms universally accepted by all 51 corporation chartering jurisdictions in the United States. However, in some states other suffixes may be used to identify a corporation, such as Ltd., Co./Company, or the Italian term S.p.A. (in Connecticut; see under Italy). Some states that allow the use of "Company" prohibit the use of "and Company", "and Co.", "& Company" or "& Co.". In most states sole proprietorships and partnerships may register a fictitious "doing business as" name with the word "Company" in it. For a full list of allowed designations by state, see the table below.

On the other hand, if you are not responsible for its tax, then you should declare the equipment in Part III of the Business Property Statement (Equipment belonging to others). Where equipment is declared in Part III of the Business Property Statement, the Assessor will also send a Notice to File to the person reported as the equipment's actual owner.