**Core Concept**
Lymphoma of the appendix is a rare condition that requires careful surgical management. The treatment of choice depends on the extent of disease involvement and the overall clinical scenario.

**Why the Correct Answer is Right**
The correct answer is **Right hemicolectomy** because it is the standard surgical procedure for addressing lymphoma of the appendix. This operation involves the removal of the right colon, including the cecum, appendix, and proximal part of the transverse colon, along with the associated lymph nodes. The rationale behind this approach is to ensure complete removal of the tumor and affected lymphatic tissue, thereby reducing the risk of recurrence.

**Why Each Wrong Option is Incorrect**
**Option B:** Extended right hemicolectomy is not typically required for lymphoma of the appendix, as the disease is usually localized to the appendix and surrounding lymph nodes.

**Option C:** Left hemicolectomy is not indicated for lymphoma of the appendix, as the disease is not typically located in the left colon.

**Option D:** Extended left hemicolectomy is also not necessary for lymphoma of the appendix, as the disease is not usually widespread to the left colon.

**Clinical Pearl / High-Yield Fact**
It is essential to note that lymphoma of the appendix is often asymptomatic and may be discovered incidentally during appendectomy for suspected appendicitis. A high index of suspicion and thorough histopathological examination are crucial in diagnosing this condition.

**Correct Answer Line**
✓ Correct Answer: A. Right hemicolectomy