According to the Partnership Act 1890, a partnership is defined as the relationship that subsists between persons carrying on a business in common with a view of profit. Alice, Bob, and Charlie have invested equal amounts of capital and agreed to share the profits equally, which indicates their intention to make a profit, despite the business making a loss. There is no legal requirement for a partnership to have a written agreement or to be registered. The fact that they agreed to share profits equally and did not explicitly agree on sharing losses does not negate the existence of the partnership. Therefore, they have been working in partnership together. 

Key Point: This question clarifies the definition of a partnership under the Partnership Act 1890. Understanding the fundamental characteristics of a partnership, including the intention to make a profit and the lack of necessity for a written agreement or registration, is essential for identifying and forming partnerships in business law.