General Electric Co. said yesterday it had signed a definitive agreement to sell its division that manufactures residential central air conditioning to Trane Co. for cash and stock worth about $161 million.

The transaction would give GE a 15 percent stake in Trane, which has been rumored for several months to be the target of a hostile takeover. Last week a Chicago securities firm revealed that it had amassed an 8.1 percent holding in Trane and is considering seeking control of the La Crosse, Wis.-based air-conditioning maker.

A GE spokesman would not specifically deny that the company was acting as a "white knight" to protect Trane's independence, but he said that the huge electrical-equipment conglomerate had been discussing a possible deal with Trane for some time.

"These discussions have been under way for several months," he said. "This deal just makes sense on the merits of the business."

The market for residential central air conditioning has been suffering along with the depressed housing market, and GE said it felt that its operations in the field would be stronger if complemented by an industrial central-air-conditioning business, which GE does not have.

A spokesman for the Justice Department said the department's Antitrust Division will review the proposed transaction.

GE, which also makes room air conditioners, would not disclose the sales volume of its central-air-conditioning operations.

Under the terms of the proposed transaction, which must be approved by Trane's shareholders, Trane will pay GE $100 million cash and 1.85 million newly issued shares of Trane stock. Trane currently has 10.2 million shares outstanding, selling at about $33 a share.

GE agreed that it would not increase its holding in Trane above 25 percent, but there are no restrictions if GE chooses to sell its Trane holdings, according to the GE spokesman. In addition, GE will put an executive on Trane's board.

Trane stock has been trading heavily since late last year, prompting speculation that it might be the target of a takeover. One rumored suitor, IC Industries Inc., denied recently that it had been purchasing Trane shares but would not comment on whether it is interested in the company.

Last week, in a filing with the Securities and Exchange Commission, O'Connor Securities, a privately held options-trading and risk-arbitrage firm, said it had bought 8.1 percent of Trane since late April--although some analysts believe that at least one other concern also has been purchasing Trane shares in recent months.